For the given functions f and g, find the indicated composition. 4 f(x) = x-8 g(x) = x (f-g)(x) 25x 4- 40x 25x 4 + 40x 4x - 32 25x 5x 4- 40x

Q: 12. f (x) = 3x − 1 \frac{f(x)-f(1)}{x-1}

A: fx=3x-1

Q: G' (x) = 2xex + x 2ex, and this is not equal to f (x). However, H'(x) = 2ex + 2xex - 2ex = 2xex = f…

A: Given Data The derivative function is G’(x)=2xeˣ+x2eˣ. The another derivative function is H’(x)=…

Q: 16. Given f (x) = x/(2+x) and g(x) = 2x/(1-x): a. Find f (g(x)) and g (f (x)). b. What does the…

A: Given functions:

Q: Find f' (2) and determine the value of x for which f'(x) = 0 a) f'(x) = ln2x - 2x b) f'(x) = (2x…

A: Two functions are given by, f'x=ln2x-2x and f'x=2x-85. The objective is to find the value of f'2 and…

Q: 1. Find the composition function a) y =f(x) = b) y = f(x) = 2x + 5x2

A: a)  given   f(x) = 1x Thus composition function of f(x) = g(x) = f{f(x)} = 11x = x

Q: snip

A: Given: fx=1x and fgx=x+1x2-x

Q: Given the functions; f(x)=3x+5, g(x)= 4-x2, and h(x)=1/x. (f+g)(x)

A: Given:  f(x)=3x+5 g(x)= 4-x2  h(x)=1/x   To determine: (f+g)(x)

Q: Given f(x) =5 -x2 and g(x) =x2+4x-12 find fg(x)

A: We are given two functions , f(x) =5 -x2 and g(x) =x2+4x-12 To start with, it is important to note…

Q: 4. Given the functions g(x) = 5x +1 find g'(x) 2х -6

A: The given function is: g(x)=5x+12x-6

Q: Given f(x)= x - x^2 and g(x)= 4x-2 Simplify f(g(x))

A:

Q: how to find the composition of (f0g)(x) f(x)=√4-x^2 and g(x)=√3-x

A:

Q: 1) f(x) = 5x and g(x) = x - 3, find f(2) + g(1)

A: Please see the below picture for detailed solution.

Q: Given the functions; f(x)= 3x+5, g(x)=4-x2, and h(x)=1/x. h(g(f(x)))

A: Gien any two functions f(x) and g(x), the composite function f of g is given by, (f o g)(x)=f(g(x))…

Q: f(x)=−4x+4​,g(x)=−5x2+5x−4​,andh(x)=−3x2+8​, find h(−1​).

A:

Q: 3. If f(x)=2x + k - 4 and f(f(k)) = 2, determine the value of f(-3).

A: f(x)= 2x+k-4 and f(f(k)) = 2, then find f(-3)

Q: Find (f-1)'(a) for f(x) = ーX-3 when a = 3x +2 (Enter an exact answer.) Provide your answer below:…

A:

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

A:

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

A: We have given  f(x) = x-2  g(x) =x2+2x g(f(x)) = g(x-2)              = x-22 + 2(x-2)              =…

Q: Let g(x) x2+4. Find a function f that produces the given composition (fo g(x)= x+8x2+27

A: (fog)(x) means f(g(x)). Plug g(x)=x^2+4.

Q: Let h(x)=f(x)+g(x). If f(x)=2x2 and g(x)=8x5, what is h′(x)? Do not include "h′(x)=" in your answer.…

A: We have been given h(x) = f(x)+g(x) and f(x) = 2x^2 and g(x) = 8x^5So we can first write a function…

Q: 13. Find [f• g](-4) for f(x) = x-8 and g(x) =-x² +2.

A: Given thatf(x)=x-8g(x)=-x2+2to find fog(-4)

Q: B. Find the domain of 1. h(x) = (x – 2) (x 2 -2 x + 1) 2. (x – 1)(x + 3) 1 and g(x) : x + 3 -1 3. If…

A: Domain is the set of all possible values of x (independent variable) for the function.

Q: 2. Let f(x) = 5x - 6 and g(x) = 7x + 3. a. Find f(g(x)). b. Find g(f(x)).

A:

Q: 1. Given f(x) = -2x and g(x) = x - 7, find g(f(2)). *

A: f(x)=-2x g(x)=x-7

Q: x + 5x Find f'(x) given that f(x) = 3x' + 4

A:

Q: Evalvate f(f(f(2) X+5 for x5

A:

Q: Make the composition (f o g) (x) with the function f (x) = x ^ 2 + 2 -2 and g (x) = √x

A:

Q: Help 1

A:

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A:

Q: Find the upper and lower limits of the function 1/3 X^3 - 3/2X^2 +3

A:

Q: For the given functions f and​ g, find the indicated composition.   ​f(x)=4x^2+2x+5​; ​g(x)=2x−3…

A:

Q: Given f-: x → x- 2 x*-1. x + 1 ' If f (k + 3) = 7, find the value of k. %3D

A:

Q: find g'(3) given that f(3) = -2, f'(3) =4, and g(x) =2x+1/f(x)

A:

Q: 19. Find the domain and range of f(x) = 2e-x +1

A:

Q: 15) f(x)= x² – 3x g(x) = 4x Find (f – g)(-1)

A:

Q: f (x) where f (x) g (x) 8x2 +24x 2x2 Find R(x) and r2 - 8x (x) 6 x2 + x -6

A:

Q: For the given functions f and g , find the indicated composition. g(x) = 2x - 5 f(x) = 4x + 2x + 8,…

A: Given that,

Q: 2 Given f(x) = x“ - 2 and g(x) 4x + 1, find a. f g b. g(f(x))

A: We will find f .g and g(f(x)) in the following step.

Q: Let f(x) = 3x2 + 3 and g(x) = 2x − 7. Find the composition. (g ∘ f)(−3)

A: Let f(x) = 3x2 + 3 and g(x) = 2x − 7. Find the composition. (g ∘ f)(−3)

Q: 1. Given f(x) S(x) = x² + 4x - 2 and g (x) = 3x – 4 , find the composition of functions for the…

A:

Q: Given the functions; f(x)=3x+5, g(x)= 4-x2, and h(x)=1/x. (fg)(x)

A: Given: fx=3x+5  gx=4-x2 hx=1x fgx is given as, fx×gx=3x+54-x2                 =12x-3x3+20-5x2…

Q: (2) for f(x)=x^2-4x+1

A: From the given data:

Q: Given the functions g(x) = 3x + 1/ 2x - 4 find g-1(x)

A:

Q: Find (fog) where f(x) = 2x^2 +x +2 and g(x) = 3x -1

A: We can find the answer as below.

Q: 2. Given f(x) = 2x² + 3x – 5 and g(x) = 4x + 7, find and simplify: a) f -g b)g¬'(f(x))

A:

Q: For the given functions f and g, find the indicated composition. f(x) = , gx) = x-7 (f-g)(x) Select…

A:

Q: 3. Find the value of the constant k that makes the function continuous f(x) = {x² – 6, x + 4k, x 6

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)? Do not…

A:

Q: f(x)=x^2-3x+9 g(x)=3x^3+2x^2-4x-9 find the (f-g)(x)

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.