Give an example of functions f and g such that f ∘ g = g ∘ f and f(x) ≠ g(x).

Q: If f:X → Y and g:Y → Z are one-to-one functions, then the composition f •g is one-to-one function.

A: f:X→Y and g:Y→Z are one-to-one function

Q: function f is defined by f (x) = |x – 2|- 3. If f(a) = f(0) and a > 0, what is the value of a ?

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Q: Let f(x) = x³ + 2, g(x) = x- - 3, and h(x) = 8x + 3. Find the rule for the function. %3D f-g

A: Given function is : fx=x3+2gx=x2-3hx=8x+3  To find the value of fx-gxhx

Q: 1 if g is the inverse of function f and f(x) = 1+x? prove that g'(x)=1+{g(x)}"

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Q: The function h() can be expressed in the form f(g(x)) where g(x) = (a +9) and f(z) is defined as:…

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Q: f (x) x + 9 and g() = x - 9,

A: (a)  fgx=fx-9=x-9+9=x (b) gfx=gx+9=x+9-9=x

Q: Find the composite function f(g(x)) if, f(x)=x³+1 and g(x)=x+1

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Q: Let f(x) = 3x + 1, x, = -1, x, = 0, x3 = 1, x4 = 2, and X5 = 3. Find E f(x,).

A: we have the given the following details   f(x)=3x+1x1=-1x2=0x3=1x4=2x5=3We have to find∑i=15f(xi)

Q: Find f + g, f - g, fg, and f/g and their domains. f(x) = 5 - x,    g(x) = x2 - 3x

A: Given, f(x)=5-x  and g(x)=x2-3x To find  f+g, f-g, fg, f/g.

Q: Calculate the composite functions f ◦ g and g ◦ f , and determine their domains. f (x) = 2x , g(x) =…

A: Composite function fog can be found with the replacement of x by g(x) whereas the composite function…

Q: Let g be a function that is defined for all x, x + 2, such that g(3) = 4 and the derivative of g is…

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Q: Let f(x) = 2x - 1 and g(x) = x2 + x - 2. Find the function: (f - g)(x)

A: fx=2x-1 and gx=x2+x-2

Q: Let f (x) = x2 - 2x, g(x) = 3x - 1, and h(x) = 1x. Find the functions. f (x) + g(x)

A: Since, we have been given that:-f(x)=x2-2x -(i)g(x)=3x-1 -(ii)and h(x)=x -(iii)Our Aim is to find…

Q: Find two functions f and g such that ( f ∘ g)(x) = h(x). h(x) = ∛(x2 − 4)

A: Given: hx=x2-43

Q: Find f + g, f - g, fg, and f/g and their domains. f(x) = x, g(x) = 2x

A: The given functions are: f(x) = x, g(x) = 2x The sum of these functions is given by: f(x)+g(x)=…

Q: Find f + g, f - g, fg, and f/g and their domains. f(x) = x,       g(x) = √x

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: If G(x) = tan x, find G(π/6), G(x - π/2), G(-x) and express G(2x) as function of G(x).

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Q: Let f(x) Determine a function 4 – x | y = g(x) so that f(g(x)) x + 3

A: Given f(x)=x+14-x

Q: domain

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Q: Find f°g and the domain of the composite function. f(x) = |x], g(x)=x+3

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Q: 19. Let ƒ(x) = x/(x-2). Find a function y = g(x) so that (ƒ ∘ g)(x) = x.

A: Given,

Q: Let f (x) = x and g (x)=|x| be two real-valued functions, O (x) be a function satisfying the…

A: Introduction :

Q: Find functions f and g such that F = fo g. (Use non-identity functions for f(x) and g(x).) F(x) =…

A: Given :  F = f o g  And F(x) = ( 9x + x 2 ) 4  Find :  f( x ) , g ( x )

Q: Discuss the continuity of the composite function h(x) = f(g(x)).

A: It is given that,  h(x)=f(g(x)) ..................(1) where f(x)=x2and g(x)=x-1

Q: 17) Let f(x) : Find a %3D X - 9 function y = g(x) so that (f •g)(x) = x. %3D

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Q: Express the function h(x) = (3x - 1)4 as a composition of two functions f and g so that h(x) = (f ∘…

A: Given: h(x) = (3x - 1)4

Q: If ƒ(a - x) = ƒ(a + x), show that g(x) = ƒ(x + a) is an even function.

A: Given that ƒ(a - x) = ƒ(a + x)To show that g(x) = ƒ(x + a) is an even function.

Q: Find the functions, f ∘ g and g ∘ f and their domains. f(x) = 2x,    g(x) = x + 1

A: Given, fx=2xgx=x+1

Q: Find f of g and g of f  f(x)= 1/x , g(x)= x+1  Find the domain of each function and each composite…

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Q: Show that if f(x) is a function satisfying f'(x) = f(x)^2, then its inverse g(x) satisfies…

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Q: Define functions f, g, and h such that F( x) = 1 /x^2 −1 = ( f x g x h)( x) and the domain of F is…

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Q: Let f(x) = x3 + 3, g(x) = x2 - 3, and h(x) = 3x + 3. Find the rule for the function. fgh

A: Use the rule of composite functions.

Q: If f(x) = x + 1 and g(x) = x – 1, – 1, (a) f(g(x)) = (b) g(f(x)) = (c) Thus g(x) is called an…

A: NOTE: Refresh your page if you can't see any equations. . . now for the function f, substitute x-1…

Q: Let f(x) = √20- x and g(x) = x² - x. Then the domain of fo g is equal to

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Q: Discuss the continuity of the composite function h(x) = f(g(x)).                                f(x)…

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Q: Let f and g be functions such that f(0)=4, g(0)=6, f′(0)=6, g′(0)=-4, Find h′(0) for the function…

A: First obtain the derivative of h (x).

Q: assume f(g(x))=x and f'(x)=1+f2(x) for all x. show that g'(x)=1/(1+x2)

A: Differentiate both sides of f(g(x))=x with respect to x. Use chain rule on the left side.

Q: The composition of the function f with the function g is written as fog and is defined by fo g(x) =…

A: Here, we have to first understand the concept of composition of function to answer the correct…

Q: Let h(x) = f(x)g(x). If f(x) = x² + 4x – 1, 9(-2) = 3, and g'(-2) = -5, what is h' (-2)?

A: Given h(x) = f(x)g(x). ƒ(x) = x² + 4x − 1, g(−2) = 3, and g'(-2) = −5,

Q: Assume that g is a twice-differentiable function (that is, g' and g" exist) and f(x) = x g(x²).…

A: The given function fx=x.gx2 Differentiate with respect to x using product rule…

Q: Let f(x)=3x-1 and g(x)=2-x2. Find f(f(x))

A: Given, fx = 3x-1  gx = 2-x2  We have to find ffx

Q: Show that f(x) and g(x) are functions by showing that f(g(x)) =x and g(f(x) = x f(x) = (x-2)^2 g(x)…

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Q: Find the composite functions f°g and g°f when f (x) : 3 %3D x+1 = and g(x) = x² – 1.

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Q: Let f(x) = x² + 2, g(x) = x-- 3, and h(x) = 8x + 3. Find the rule for the function. %3! %3D %3D f-g

A: Consider the given function as, fx=x3+2, gx=x2-3 and hx=8x+3

Q: Find functions f and g so that h(x) = (f • g)(x). h(x) = 2 %3D x-2 f(x) = 1/x, g(x) = x²-2 f(x) =…

A: Given: hx=fogx and hx=1x2-2 hx=fogx=fgx  So, fgx=1x2-2 Check fgx for each given option (i) fx=1x,…

Q: Find f such that f'(x) = x - 5 and f(0) = 3. f(x) = %3D

A: Given: f'x=x2-5 f0=3   Integrate the function with respect to x. ∫f'x=∫x2-5dxfx=∫x2dx-5∫1dx=x33-5x+C

Q: Express the function,h(x) =1/(4x + 5) as a composition of two functions f and g so that h(x) = (f ∘…

A: here given as hx=fogx=14x+5

Q: it) Let f(x) = x² + 1 and g(x) = x² – 1 %3D - Then (f• f)(x) = (f°g)(x) = (g • f)(x) =

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Q: Let f (x) = x and g (x) =|x| be two real-valued functions, O (x) be a function satisfying the…

A: Introduction :Here we have two function f(x) = xand g(x) = |x| . and another function ?(x) also a…