use each set of functions to find f(g(h(x))). Simplify your answers. Given f(x) = 1/ x , and g(x) = x − 3, find the following: a. (f ∘ g)(x) b. the domain of(f ∘ g)(x) in interval notation c. ( g ∘ f )(x)

Q: Find the domain of the function. G(x) = √(1 - x)

A: To find the domain of the function

Q: What value should be assigned to a to make the function S(x) = (x²-1, x<3 (2ax, x 23 Continues at…

A:

Q: Express the given function h(x) = l3x - 4l as a composition of two functions f and g so that h(x) =…

A: Given :h(x) = 3x -4To express h(x) as a composition of two function f and g so that  h(x) = (f∘g)(x)…

Q: Express the function,h(x) =1/(2x - 3) as a composition of two functions f and g so that h(x) = (f ∘…

A: We will take the inner function as g(x) and the outer function as f(x). Note that 2x-3 is inside.…

Q: Use the functions f(x) = x + 4 and g(x) = 2x − 5 to find the given function.

A:

Q: given f(x)=1/x and f/g)(x)= x-6/x2+4x, find the function of g

A:

Q: find functions f and g so that f ∘ g = H.

A: H(x)=2x+1

Q: Graph the function f(x) = 4x + 2 and determine the interval(s) for which f(x) ≥ 0.

A:

Q: Express the given function h(x) = (2x - 5)3 as a composition of two functions f and g so that h(x) =…

A:

Q: Evaluate the function at the given expression. f(x)=x2−3x f(x−1)=

A:

Q: For which interval does the function f(x)=x^3−x^2+1 have an inverse?

A:

Q: Find the value of k that will make the function f(x) continuous. -x2+8, if x+ 3 f (x) =, k, if x=3

A: topic - limits and continuity

Q: Determine f (x) for each of the given function. f (x) = 2x 3 -

A: SOLUTION-

Q: What type of discontinuity does the function f(x)=xsecx have?

A:

Q: Find constants a and b, such that the function following function is continuous for -3 <x <0. -x +1,…

A:

Q: Given f(x) = sqrt{x} and g(x) = |x − 2|, find g/f. Determine the domain of the function in interval…

A:

Q: When written as y = f1x2, a function is said to bedefined .(a) explicitly (b) consistently(c)…

A: y = f1x2

Q: If f(x) = Vx +1 , g(x) = Vx – 1, find the domain of f +g. %3D

A: Domain is set where function is defined

Q: Give the interval where f is decreasing and the interval where f is increasing for the given…

A: Given function

Q: Graph the function f(x) = 9 − x2 and determine the interval(s) for which f(x) ≥ 0.

A:

Q: Given f(x) = √x and g(x) = |x − 3|, find g/f . Determine the domain for each function in interval…

A:

Q: Find the value of k, if the constant k that makes the function continuous:

A: Given,          f(x)=x2+k2if x≤4kx+12if x&gt;4

Q: find functions f and g so that f ∘ g = H.

A: A function defines a relationship between two sets, where one set is dependent on other set. Any…

Q: Use the functions f(x) = x + 4 and g(x) = 2x − 5 to find the given function.

A:

Q: Find the domain of the given function.

A: Domain is set of all the input values which can take value in function such that it gives some…

Q: Evaluate the function at the given expression. f(x)=x2−3x f(x−1)

A: Given that fx=x2-3xTo find :fx-1Solution :Replace  x to x-1fx-1=x-12-3x-1

Q: For the function f (x) = V8 (x – 1)*, find f-'(x).

A: Given query is to find the inverse of the function.

Q: Find the domain of the following function. f(x) = V3x – 45 (Зх — Give your answer in interval…

A: Given : fx = 3x-45

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: Let f(x) = 4 - x2 and g(x) = x + 5. a. Find ( f ∘ g) (x).   b. Find f(x + h) - f(x)/h, h ≠ 0, and…

A: Given:fx=4-x2gx=x+5Formula:f∘gx=fgxf'x=fx+h-fxh

Q: If f(x) : = x + 9 and h(x) = 2x – 4, find a function g such that g of = h. g(x) =

A:

Q: g(x) = x2 + 2x – 2 I

A:

Q: Find and simplify f{a + h) – {a), (h ± 0) for the function. f(x) = 4x2 - 10x + 1

A:

Q: Graph the function. f(x) =. * for x<0 x+3, for x20 Choose the correct graph below. OA. OB. OC. OD.

A: Given, fx= 18x      for  x &lt;0x+3   for   x ≥ 0  We have to graph the function.

Q: Find the domain and range respectively for function 1+x2

A: The given function 1+x2

Q: Q1:- Find the domain of the following functions: a) f(x) = |x|+

A: See the attachment

Q: Given the functions defined by f(x) = 3x² – 2 and g(x) = x² – 2, calculate the following: (f •…

A: Ans:Given,fx=3x2-2 and gx=x2-2we have to find fog-2

Q: Find f if f ' (x) = e x  + 20 ( 1 + x 2  ) -1  and f (0) = -2

A:

Q: Find f'(x) when f(x) is written in the following form: (x² – 3x + 2)z f(x) (x² – 9)Ž

A:

Q: B. Find the domain of each function. 1. f(x)=1+x 2. f(x)=1- 3, h(x)= -4

A: We find domain of given functions from 1-3(as by Bartleby policy I have to solve first 3 subparts)…

Q: b. Suppose the function h is defined as h(x) = 3f(x). Determine the domain and range of h.

A: b. Given that  h(x)=3f(x) Domain of f is [0,4] and range [0,2]

Q: Given f(x)=√(2−4x) and g(x)=−5/x find g ° f the domain of (g∘f)(x) in interval notation.

A:

Q: Given the function f(x) = 1/1+x^2, x ≥ 0, determine the value of (f^−1)′(1/2). Give your answer in…

A: f(x)=11+x2

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

A:

Q: For the function f(x) = x` find f"(x), f'(0), f"(1), and f"(- 1).

A:

Q: Express the function h(x) = (x2 + 2x - 1)4 as a composition of two functions f and g so that h(x) =…

A: To express  function h(x) = (x2 + 2x - 1)4 as a composition of two functions f and g so that h(x) =…

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: Find the domain of the following function using interval notation f(x) = X - 6 O A. (-00, 0) O B.…

A: