Express the function G in the form f ∘ g. (There is more than one correct answer. The function is of the form  y = f(g(x)). Use non-identity functions for f(x) and g(x).) G(x) =  1 x + 3 (f(x), g(x)) =

Q: Express the given function h as a composition of two functions f and g so that h(x)= (f o g)(x),…

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

A: h(x) = |3x - 4| To write h(x) as a composition of two functions f and g so that h(x) = (f ∘ g)(x)…

Q: The function f(x) = can be written as g(h(x)). One 4-x2 possibility for g(x) and h(x) is: g(x) = Ar…

A: we have to find out composition function

Q: Find the domain of the function. h) - 5) X - A) {x|x 0}, or (0, -) B) {x|x 1), or (-, 1) u (1, ) D)…

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Q: Let h(x)=f(x)g(x). If f(x)=x2−3x,g(0)=−1, and g′(0)=−4, what is h′(0)?

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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: Find the domain of the function : g(x) =1/(x2 + 1) - 1/(x2 - 1).

A: The domain of  rational function is the set of all real numbers except those for which the…

Q: If f(x)= 2x-and g(x)=3x+1, what is f(x)-g(x)+g(x)²? O8x6+9x2+3x O8x+9x-x O8x+9x2-3x O8x+9x+x

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Q: If f is a differentiable function and such that and g (x) =x^2 f(x) such that f(3) = -7 f'(3) = 2,…

A: This question can be solved using the concept of product rule of differentiation.

Q: If f and g are differentiable, then f g is differentiable.

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Q: 1. Use f(x) = 5-x and g(x): to find the following and identify its domain: %3D x-2 a) (f g)(x) b)…

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Q: Let k(x)=f(x)g(x)h(x). If f(x)=−3x+4,g(x)=−x+4, and h(x)=−3x2−4x+3, what is k′(x)?

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Q: xpress the given function h as a composition of two functions f and g so that h(x)=(f•g)(x),where…

A: Given data: The expression for h(x)=(x4-6)1/7. The given one of the function is (x4-6). The…

Q: Find the value of a for which the function x²–1 x+1 ' x# -1 f(x) = а, x = -1

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Q: Let k(x)=f(x)g(x)h(x). If f(x)=−2x−3,g(x)=−3x+3, and h(x)=−3x2+x+1, what is k′(1)?

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Q: Let h(x)=f(x)+g(x). If f(x)=x4 and g(x)=6x3, what is h′(−3)?

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Q: Let h(x)=f(x)g(x). If f(x)=−2x2+2x+3 and g(x)=−x2−3x−4, what is h′(−1)?

A:

Q: Let k(x)=f(x)g(x)h(x). If f(x)=3x−2,g(x)=2x−3, and h(x)=−2x2+4x, what is k′(1)?

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Q: The function f(x) = x²e*- ex has a root in [0,2]

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Q: Let h(x)=f(x)g(x). If f(x)=x2+4x−1,g(−2)=3, and g′(−2)=−5, what is h′(−2)? Do not include "h′(−2)="…

A: We have to find

Q: 2. If f(x) = x - 2 and g(x) = x2 + 2x, what is the composition g(f(x))? A) x2 - 2x B) x3 - 4x…

A: Given  f(x)=x-2g(x)=x2+2x To find g[f(x)]

Q: The domain of the function f (x, y) = In(2 – /x² + y² ) is:

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Q: (a) g(x) = x + 1 x-1 (using the definition)

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Find  f + g,   f − g,   fg,  and  f/g  and their domains. f(x) = 5 − x,    g(x) = x2 − 4x

A: Since you have asked a question with multiple question in a single request, we would be answering…

Q: Please show step-by-step solution

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Q: Find ao of the function f(x)=(-x)², 0≤x≤ 2π

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Q: The function h(x) 1 can be expressed in the form f(g(x)) where g(x) = (x + 7) and f(x) is x + 7…

A: Given ,  The function h(x) = 1/(x+7) can be express es in the form f(g(x)) where g(x) = (x + 7)  We…

Q: (=)= The domain of the function f = e va-2 is a) [2, 00), or, equivalently, {x > 2}. O b) (2, 00),…

A: The solution is given as

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

A:

Q: The function h(x)=1x+7h(x)=1x+7 can be expressed in the form f(g(x))f(g(x)) where…

A:

Q: that f(x)=x^2+11x+18f(x)=x2+11x+18 and g(x)=x+2g(x)=x+2, find f(x)-g(x)f(x)−g(x) and express the…

A: Given , fx=x2+11x+18  and gx=x+2Now , fx-gx=x2+11x+18-x+2                         = x2+11x+18-x-2…

Q: 3. Find (f-g)(x) if f(x) = 22 +x+1 and g(x) = x2- r - 1. %3D %3D

A: Given, f(x)=x2+x+1g(x)=x2-x-1

Q: Find functions f and g so that h(x) = (f g)(x). 8 3) h(x)= N8x+2 A) f(x) =8/x, g(x) = 8x+2 C) f(x)…

A: We have to find f and g so that  hx=fogx Now, hx=88x+2 we know that composite function fogx=fgx…

Q: Let g(x) = x"3. Show that g' (0) does not exist. If a + 0, find g' (a) g'(a) =

A: We use the power rule to find g'(x)

Q: Express the given function h(x) = 3√(x2 - 9) as a composition of two functions f and g so that h(x)…

A: Given function is  h(x)= x2-93.

Q: Let h(x)=f(x)/g(x) where f(x)=x^2+5x−1, g(2)=−4, and g′(2)=−2 what is h′(2)?

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Q: 6) Find the value of c such that {0, c} is 2-cycle such that c be a constant and let the function be…

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Q: Let h(x) = f(x)g(x). If f(x) = 2x² +1, g(1) = 0, and g'(1) = –1, what is h' (1)? Do not include…

A: Given, hx=fxgx where fx=2x2+1, g1=0  and  g'x=-1 Put x=1 in f(x) f(1)=212+1f(1)=3 The derivattive of…

Q: The fixed-points of f(x) = (x² + 2) a and

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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: Let h(x)=f(x)g(x) where f(x)=2x^2−4x, g(−2)=4, and g′(−2)=−5 what is h′(−2)?

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Q: Let h (x) = f(x) g(x). If f (x) = x² + x and g(x) = -2x² + 4x - 1 what is h' (0)?

A: NOTE: Refresh your page if you can't see any equations. .

Q: If (2)-3.f(2)-1, g(x)=1/x, and htx)-[fx)][g(x)], then what is h'(2)?

A: Given that h(x)=[f(x)][g(x)] So, using the product rule,  h'(x)= [f'(x)][g(x)] + [f(x)][g'(x)] Then…

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

A: Given functions,  f(x) = x2 + x,       g(x) = x2 To find f + g, f - g, fg, and f/g and their…

Q: The function h(x)=1 (fraction) x+9 can be expressed in the form f(g(x)), where g(x)=(x+9), and f(x)…

A: ANSWER : f(x) = 1/x   EXPLANATION :

Q: 5) Given f(x )-3x - 5 and g(x) = 2x - 11, Find g(f(x)). %3D Substitute f(x) into the x of the gfx)…

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Q: Let h(x)=f(x)g(x). If f(x)=−3x 2−4x+2 and g(x)=−x2 +3x+2, what is h′(−1)? Do not include "h′(−1)="…

A: Consider the function

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.