Find a power function, f(x), satisfying the following. a) The points (2, 2) and lie on the graph of fx) = b) x 2 3 5 f(x) 128 972 12500 f(x) = %3D

Q: The function f is defined by f(x) = 2x +1. Find f(5x). f(5x) = 0

A: We can find f(5x) as below.

Q: Find the requested function and state the domain. 6 (g o f)(x) for f(x) = and g(x) = 2-x 6

A: Given : fx = 6x6gx = 2-x

Q: (1 point) Let f(x) = x² – 6x and g(x) = x – 6. Evaluate the following - %3D 1. (fo g)(x)= 2. (go…

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Q: 3) Find domain of the following functions x+4 a) f (x) = x²+2x-8

A: Given function is: fx=x+4x2+2x-8 We have to find the domain of f(x).

Q: Suppose that f(x) = (x - 4)*.

A: At the point of inflection, f''(x)=0.

Q: What is the vertex of the following function? f(x) = x² + 4x +3 (-1,4) (-2,-1) (4,3) (-4, 3)

A: Solution : Given that f(x) = x^2 + 4x + 3 For vertex of the given function , f'(x) = 0

Q: Let f(x) 1 and g(x) За + 8. с — 2 Find each of the following: 1 a) f(g(6)) 24 b) f(g(x))

A: Given, f(x)= 3x+6 g(x)= 5x²+7x We know that, (g°f)(x)= g(f(x)) Substituting known values, = g(3x+6)…

Q: Create a table of value for f (x) = x and showcase how you got those values.

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Q: :) is one-to-one and f(11)=-9, then f(-9) = (f(11))-l =

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Q: Find the domain and range of the given 9) function. m(x) = -/x - 3

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Q: Find the range of the function f(x) = 1/3x-5, if the domain is { -3, 0, 6}

A: f(x)=13x-5Domain is -3,0,6substitute x=-3f(-3)=13(-3)-5=1-9-5=-114

Q: 6- Do a complete analysis to sketch the following function. F(x)=2x-x²/x²-2x+1

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Q: If f (x) =ax³+ bx² , determine a & b so that the graph of f will have a point of inflection at (1,2)

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Q: Rewrite each pair of functions. (g) and g(t), as one composite function, f(g(e)). (If not possible,…

A: To find f(g(t))

Q: f(x) = x3 + 3x

A: if first derivative is positive in the that interval f(x) is decreasing

Q: Let f : R → R, where f(n) = 5 . Answer the following questions. 7x²+3*

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Q: Find the function g such that fog = In (4x³ +9) if f(x)= Inx g(x) = ...

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Q: Find the f(x) = 4x + 1, g(x) = 6x - 2 (a) (f + g)(x) = (b) (f- g)(x) = (c) (fg)(x) = (d) (f/g)(x)…

A: Given f(x)=4x+1   and g(x)=6x-2