=8. If f(x) and g(x) = x2-4, then what is f(g(-2))? x+ 4

Q: 4. If [æf (x) + 2] dæ = x³ – a² then find the function f (x). 3 A) 2 3 B) 2+ C) 3- 2 E) 2– D) 3+ --…

A: The given equation is x∫x fx+2dx=x3-x2.

Q: 3. Given that f(x) = 3x +3 and g(x) = 2x -6. Determine g[f(x)] %3!

A:

Q: 2. If f(x) = e*+ °, what is f"(x) ? x'+ 5

A: Given that f(x)=ex2+5 find out f11x

Q: 1. If f(x) = x-1 and g(x) = 2x, what is g(f(x))? c. 2x -1 %3D а. х-2 b. 2х-1 d. 2x-2

A:

Q: #9: Suppose you have a function f (x) that has x intercepts as -3, 1, and 5. If f(0) = -20, what can…

A:

Q: x2-8 If fx)= X-4 where is f not differentiable?

A: Given the function

Q: 1 if x -2 18. f(x) = x + 2 %3D a = -2 1 if x -2 x+3 if x -1 a = -1

A:

Q: 1. if f(x)= x2-4,  g(x)=x3 , F(x)=1/(x-3) a. F(g(y)) b. f(square root of x4+2)

A: F(g(y)) can be obtained by replacing x by g(y) in F(x)

Q: 13 Given that f(x)= 2x+1 and h(x)=x, find (h o f)(3).

A:

Q: Suppose g'(x)=sec^2(x) and g(0) = 0. What is g(x)?

A:

Q: Let h(x)=f(x)g(x) where f(x)=2x2−4x, g(−2)=4, and g′(−2)=−5 what is h′(−2)?

A:

Q: 7. Iff (1) = 5, which could be the equation for f (x)?

A:

Q: If g(x) = max {x, 1/x} what is g(x) when x ϵ N2 (.5)?

A:

Q: 1. Solve for (f1)'(3) if f(x) = x³ + x +1

A: Recall:  d(f-1(a))dx=1f'(b)                ................(1) How to find Derivative of the…

Q: f(x)=x2g(x). If g(2)=3 and g'(2)=-2, find f'(2)

A: Given that,…

Q: 2 Find f(x)- g(x) when: f(x) = x2 + 1 g(x) = 2x – 5 x? + 3x – 3x x² - 2x + 6 -x? + 2x + 4 x? - 2x –…

A:

Q: ,if 0<x< n2 ) = }e** ,if 0 < x <n2 0, otherwise 8x+2 f(x) :

A: The range of x is (0 π^2), is it right?

Q: If f'(x) > 3 for all x and f(2) = 5, what can you conclude about f(4)? %3D

A:

Q: Graph the function

A:

Q: x+6 if x 2

A: Given that: f(x)=32x+6x&lt;-24-x2-2≤x≤2-(x-2)2x&gt;2

Q: 2. If f(x) = g(x) × h(x) and f'(x) = -2(x – 7) + 1(-2x – 6) , find a possible equation for f(x)

A: see below the answer and explanation

Q: (x -1, if 0 < x < 1 2x f(x) = |x – 3| , g(x) = -4 Vx, h(x) = %3D , if

A:

Q: ? Suppose that * f(3) = 1, and f(x) > 0, and f(x) < 0. Is it possible that f(2) = 3 4

A: Given fι 3=12  and    fιx&gt;0and fιιx&lt;0 . it is possible that fι2=34let g3 =  fι 3=12    ,…

Q: 17. If f(x - 1)+ 2/(1 — х) %3 3х, what is f(x)? А) -Зх + 1 В) х—3 С) -х +3 D) -3x – 1 |

A:

Q: (8) If f(x) = x² – 3x, what is f(x +h) - f(x) =? h (x² + 2xh + h²)-3(x+h)-(x²-3x) = 2x – 3 + h (x² +…

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)?

A:

Q: What are the critical points for the function f(x) = x³ + 6x² – 36x + 7. %3D

A:

Q: 4. If f(x) = -2*43 find X-1

A:

Q: If f(x)= x – 4 and g(x)= Vx – 2; | f which of the following is equal to (x)?

A: Rational function value

Q: If f(x)=5x-1, g(0)=2, g'(0)=4, and h(x)=f(g(x)), then what is h'(0)?

A: Given that h(x)=f(g(x)) Using chain rule we get: h'(x)= f'(g(x))g'(x) We plug x=0 So, h'(0)=…

Q: 19) If f(x) = 3x + 1 and g(x) = 5 – x°, find g(f(x)).

A: Given:

Q: 10. Given the functions /(x) = 3x² + 2x + x+1 and g(x) = 2x² – 1, find (f - 9)x. a 3x +x b. 3x +x+2…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: If f(x) = 3 + 2x and g(x) = square root of 4 + 4x Then, what is the composite function of f o g?

A: Given: - The functions are, f(x)=3+2x and g(x)=4+4x To find: - The composite function of f∘g

Q: Find h'(-3) if h(x)=4g(x)-5f(x), f(-3)-7,and g'(-3)=-2. Oh'(-3)-0

A:

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

A: Given:h(x)-f(x)g(x)f(x)=-3x2+2x-3g(x)=-3x2+4x+3

Q: Derivatives

A:

Q: For what value of the constant c is the function f continuous on (-0, ∞)? ( cx2 + 8x if x < 5 f(x)…

A: Given f(x) = cx2+8x   if x&lt;5x3-cx  if x≥5               we find the constant C is the function f…

Q: Suppose F(2) = 1, F(8) = − 1, and F'(x) = f(x). - 10 [ f(x) dz = 10

A:

Q: f(x) = x* – }x' – x + 2x –1 -

A: Given   f(x)= 14x4-23x3-12x2+2x-1has turning point at where the f'(x)=0differntiate f(x) with…

Q: 3. For f(x) = x - 10, find the solution to f(x) = 5.

A: f(x) = x - 10 f(x) = 5

Q: 1. If f(x) = 3x + 9 and g(x)=x²-4, find: a) (fog)(x) c) (gof)(x)

A: A detailed solution is given below

Q: -8- -7 -6- 5- y = f (x) 3- -2 sy = g(x) LO 4-

A:

Q: 3- For what value of c is the function continuous? Provide a well- communicated solution. F(x) = {…

A:

Q: 4) f(x) = ! g(x) – - - - 3

A:

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)?

A:

Q: For what value of x does  function g(x)= (-1/3)x^2+2x^2 convex?

A: please see the next step for solution

Q: .If f (x) = 5x - 2, g (x) = 2x - 3 and h (x) = x2, then (fogoh) (-1) =

A:

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…