Explanation f (x) = (x −2)2;Get stepbystep solutions from expert tutors as fast as 1530 minutes Your first 5 questions are on us!Transcribed image text Given that f(x) = 462 – 5 (where f(x) = y) and g(x) = f(x), complete each of the following a Evaluate f(3) f(3) = 1 Preview b Solve f(x) = 76 for 2 x = 56 Preview c Evaluate g( – 3) 91 – 3) = 1/2*18 Preview Submit License Question 18 Points possible 3 Unlimited attempts Score on last
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F 4 if g x 2 x brainly-In mathematics, a function (or map) f from a set X to a set Y is a rule which assigns to each element x of X a unique element y of Y, the value of f at x, such that the following conditions are met 1) For every x in X there is exactly one y in Y, the value of f at x;2) If x and y are in X, then f(x) = y;
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The Algebra of Functions Like terms, functions may be combined by addition, subtraction, multiplication or division Example 1 Given f ( x ) = 2x 1 and g ( x ) = x2 2x – 1 find ( f g ) ( x ) and ( f g ) ( 2 )Learn how to solve f(g(x)) by replacing the x found in the outside function f(x) by g(x)Proof of f(x) g(x) = f(x) g(x) from the definition We can use the definition of the derivative
Question Find f ∘ g and g ∘ f f(x) = x 4 , g(x) = x2 (a) f ∘ g (b) g ∘ f Find the domain of each function and each composite function (Enter your answers using interval notation) domain of f domain of g domain of f ∘ g domain of g ∘ fGiven f (x) = 3x 2 – x 4, find the simplified form of the following expression, and evaluate at h = 0 This isn't really a functionsoperations question, but something like this often arises in the functionsoperations contextIf f(x) = 2x^3 3x^2 4x 1 and g(x) =3
We let g(x)= x2 and h(x) = sinx so that f(x)= g(h(x)) Then g (x) = 2x, g (h(x)) = 2sinx, and h (x) = cosx, so we have f (x) = g (h(x))h (x) = (2sinx)(cosx)= 2sinxcosx = sin2x ThePowerRule g(x) n = n g(x) n−1 g (x) Example4a Find f 4(x) if f(x)= 3 √ x x2 1 We write f(x)= (g(x)) 1 3 where g(x)= x4 x2 1 Then f (x) = 1 3 (g(x))− 2 3 g Answer is (2) g (x) = x2 x 1 g (f (x)) = 4 x2 10x 5 = (2x 2)2 (2 2x) 1 = (2 2x)2 (2 2x) 1 ⇒ f (x) = 2 2x f (5/4) = 1/2 Please log in or register to add a comment ← Prev Question Next Question →X!2 g(x) = 2(2) 0 5 = 4 5 (b) lim x!2 f(x) h(x) (c) lim x!2 f(x)h(x) g(x) Note 1 If lim x!ag(x) = 0 and lim x!af(x) = b, where bis a nite number with b6= 0, Then the values of the quotient f(x) g(x) can be made arbitrarily large in absolute value as x!aand thus 1 the limit does not exist
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Here, value of a = 4 and b = 2>1 From the above definition, as we increase x, f(x) Yintercept ( plug x =0 to solve for y) Substitute the value of x =0 in given equation;And "f" is just a name These are all the same function f(x) = 1 − x x 2;F (g (2)), g (x)=2x1, f (x)=x^2 \square!
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Pumpkin(θ) = 1 − θ θ 2F (g(x)) f ( g ( x)) Evaluate f (g(x)) f ( g ( x)) by substituting in the value of g g into f f f (x2) = 3(x2)−4 f ( x 2) = 3 ( x 2) 4 Simplify each term Tap for more steps Apply the distributive property f ( x 2) = 3 x 3 ⋅ 2 − 4 f ( x 2) = 3 x 3 ⋅ 2 4 Multiply 3 3 by 2 2 f ( x 2) = 3 x 6 − 4 f ( x 2G(x) = x 3 f (g(4)) = f (4 3) = f (7) = (7 −2)2 = 52 = 25 Answer link
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Re If f(x) = 2x— 2 and g(x) = 4 — x, then f(g(x)) = g(f(x)) for , 1009 Expert Reply Post A Detailed Correct Solution For The Above Questions And Get A Kudos Let f(x)=4√x If g(x) is the graph of f(x) shifted up 3 units and right 2 units, write a formula for g(x) g(x)=Question 7649 F(x) =x^22x4 ;
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Find (fg)(x), (fg)(x), (f*g)(x) and (f/g)(x) for each f(x) and g(x) 2 f(x)= 8x^2 g(x)=1/x^2 I'm having trouble understanding what i have to do, please help This question is from textbook Algebra2 Answer by jim_thompson5910() (Show Source)Given f ( x) = 2 x 3 and g ( x) = – x2 5, find ( f o g ) (1) First, I'll convert this to the more intuitive form, and then I'll simplify ( f o g ) (1) = f ( g (1)) Working bitbybit, since g (1) = – (1) 2 5 = –1 5 = 4, and since f (4) = 2 (4) 3 = 8 3 = 11, then ( f o g ) (1) = f ( g (1)) = f (4) = 11The "x" is just a placeholder!
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Stack Exchange Network Stack Exchange network consists of 178 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build If g(x) = x2 x – 1 and g(f(x)) = 4x2 – 10x 5, then find f (5/4) (1) 1/2 (2) 1/2 (3) 1/3 (4) 1/3 Welcome to Sarthaks eConnect A unique platform where students can interact with teachers/experts/students to get solutions to their queriesSolution for If f(x) = (1 − x)2 and g(x) = 4 − x, find f(g(x)) and g(f(x)) Q Assume that the probability of the birth of a child of a particular sex is 50%In a family with six A Probability of girl = 05 Probability of boy = 05 Also the birth of boy and girl is independent
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From the chain rule of composition of functions we have (fog)'(x) = f'(g(x)) g'(x) In the given problem f(g(x)) = x^2x, therefore (f(g(x))' = 2*x1 = f Transcript Example 16 Let f(x) = x2and g(x) = 2x 1 be two real functions Find (f g) (x), (f – g) (x), (fg) (x), ("f" /𝑔) (x) f(x) = x2 & g(x) = 2x 1 (fNote If f takes its values in a ring (in particular for real or complexvalued f ), there is a risk of confusion, as f n could also stand for the nfold product of f, eg f 2 (x) = f(x) f(x) For trigonometric functions, usually the latter is meant, at least for positive exponents 12
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Free functions composition calculator solve functions compositions stepbystepFxgx=x\sqrt {x1} f x g x = x x − 1 Subtract gx from both sides Subtract g x from both sides fx=x\sqrt {x1}gx f x = x x − 1 − g x The equation is in standard form The equation is in standard form xf=gxx\sqrt {x1}G(x)=v(9x) (When I do v() that is a square root symbol) Find each of the following if it exists My question is (fg)(7) (7^2(2)(7)4)(v(9(7)) ()(v(16)) (59)(4)236 I'm wondering if I figured this out correctly The minus negative 7 in the square root is throwing me off I dont understand if i
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3) If x and y are in X, then f(x) = f(y) implies x = y;If v (x) is larger of e x − 1 and (1 x) lo g (1 x) for x ϵ (0, ∞) then l o g (v (8) 1) is equal to View solution Let f ( x ) = 2 x tan − 1 x , g ( x ) = lo g ( 1 x 2 ) , h ( x ) = sin x u ( x ) = x − 6 x 3 1 2 0 x 4Let f(x) = g(x) (x 1)(x 2)(x – 3)°(x – 4)³, where g(x) = x bx² cx d If f(x) is differentiable for all ER and f'(3) f"(4) = 0 then the value of g(5) is
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Let f(x)=4√x If g(x) is the graph of f(x) shifted up 3 units and right 2 units, write a formula for g(x) g(x)= algebra 2 The graph of g(x) is the graph of f (x)= x^2 shifted 4 units left, vertically stretched by a factor of 3, then shifted 5 units up What is the function rule for g(xW(A) = 1 − A A 2; Get an answer for 'Let F(x)=f(f(x)) and G(x)=(F(x))^2 You also know that f(8)=4, f(4)=3, f'(4)=3, f'(8)=6 Find F'(8) and G'(8)' and find homework help for other Math questions at
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If a horizontal line intersects the graph of f(x)inmorethanonepoint, then f(x)isnotonetoone The reason f(x)wouldnotbeonetooneisthatthegraphwouldcontain two points that have the same second coordinate – for example, (2,3) and (4,3) That would mean that f(2) and f(4Answer to f(x) = x^2 2 and g(x) = x 4, find (f o g)(2) and (g o f)(1) 1 (f o g)(2)= 2 (g o f)(1)= By signing up, you'll get thousands ofCompute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history
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Example 16 Let F X X2 And G X 2x 1 Find F G Fg F G
F(q) = 1 − q q 2;G(x) = f (x k), can be sketched by shifting f (x) k units horizontally Vertical Stretches and Shrinks For the base function f (x) and a constant k > 0, the function given by g(x) = k f (x), can be sketched by vertically stretching f (x) by a factor of k if k > 1 orFind f(g(x)) f(x)=1/(x2) g(x)=4/x Set up the composite result function Evaluate by substituting in the value of into Simplify the denominator Tap for more steps Factor out of Tap for more steps Factor out of Factor out of Factor out of To write as a fraction with a common denominator, multiply by
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Solution for g(x)=4f(x) equation Simplifying g(x) = 4f(x) Multiply g * x gx = 4f(x) Multiply f * x gx = 4fx Solving gx = 4fx Solving for variable 'g' Move all terms containing g to the left, all other terms to the right Divide each side by 'x' g = 4f Simplifying g = 4fI'm a little stuck with this simple function If ${f(g(x)) = 4x^28x}$ and ${f(x)=x^24}$, then what's the value of ${g(x)?}$ Any tips?Answer If f(x) = 4 – x 2 and g(x) = 6x, then (g – f)(3) = 23 Let us solve it step by step Explanation Given that, f(x) = 4 – x 2 and g(x) = 6x, Both f(x) and g(x) are function of x and depend on x (g – f)(x) = g(x) f(x) Substituting the values of g(x) and f(x) we get, = 6x (4 x 2) = 6x 4 x 2 = x 2 6x 4 Solve this for
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Explanation This is a composition of functions f (x) = x −3 g(x) = x2 4 f (g(x)) = f (x2 4) = x2 4 − 3 = x2 1 The range is f (g(x)) ∈ 1, ∞ g(f (x)) = g(x − 3) = (x −3)2 4 The range is g(f (x)) ∈ 4, ∞ Answer linkComposite Function A composite function is a function which is made by combining two or more than two functions For example, if {eq}f(x) {/eq} and {eq}g(xYintercept (0, 4) Therefore, the only correct option is C because if we increase the value of x, the function f(x) tends to negative infinity and also it cut the yaxis
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22ffx 2 − 2f − f x View solution steps Solution Steps g ( x ) = f ( x 2 ) 2 g ( x) = − f ( x 2) 2 Use the distributive property to multiply f by x2 Use the distributive property to multiply − f by x 2 \left (f\right)x2\left (f\right)2Click here👆to get an answer to your question ️ If g(x) = x^2 x 1 and (gof)(x) = 4x^2 10x 5 , then f (54) is equal to4) For every x in X, there exists a y in Y such that f(x
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