f(x) = x2,    g(x) = x + 8 Find (f ∘ g)(x).       Find the domain of (f ∘ g)(x). (Enter your answer using interval notation.)

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

A: To find the domain of the function

Q: Determine (algebraically) whether the given function is even,odd,or neither.

A: To determine (algebraically) whether the given function is even, odd, or neither. f(x)=x1+x2

Q: The domain of the function f (x) = x/x - 2 consists of all x ∙ 2.

A: We have to find domain of the function fx=xx-2 We can see this function is defined for all real…

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: If f and g are both even functions, is f + g necessarily even? If both are odd, is their sum…

A:

Q: a) Find the intervals at which the function is increasing or decreasing. x2 f(x) = 16 – x2

A: f(x) = x²/(16 - x²) So, f'(x) = [(16 - x²)•2x - x²•(-2x)]/(16 - x²)²  So, f'(x) = 32x/(16 - x²)²…

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

A: H(x)=2x+1

Q: Let f(x) = x -9, g(x) = /x + 9, and h(x) = 6x² - 9. Find the rule for the function. %3! gh f

A: Since, f(x)=x-9, g(x)=x+9 and h(x)=6x3-9.Our Aim is to find the rule for the function ghg-f.

Q: If f(x) and g(x) are two functions defined by f(x) = √(x + 1) g(x) = | x - 1 |, then what is the…

A: To find f(g(9))

Q: In general, (fg)' is not equal to f' g', but let f (x) = e3x and find a function g such that (fg)' =…

A:

Q: Determine the open intervals on which the function f(x) = √(x2 − 1) is increasing,decreasing, or…

A: f(x)=x2-1

Q: The function f(x) = x/(x - 2) is one-to-one. Find f -1

A: Given the function fx=xx-2 is one-to-one. To find: f-1 Solution: Given function can be written as:…

Q: Can a function such as f (x) = 53x be written in the form f (x) = bx? If so, what is b?

A: Comparison of the functions helps to determine the validity of the statement. The given function is…

Q: Find the domain and range of the function f(x)=: 1+x

A: Here I am attaching image so that you understand each and every step.

Q: Find the open intervals on which the function is increasing or decreasing.

A: Given: f(x)=(x-1)2(2x-5)

Q: Let f (x) = → 1 and g(x) = 3 – Va. Find the domain of (f· g)(x).

A: .

Q: Evaluate the function ( f − g)(1) for f(x) = x + 3 and g(x) = x2 − 2.

A: To Evaluate the function ( f − g)(1). Given that the functions are f(x) = x + 3 and g(x) = x2 − 2.

Q: For the function f defined by f(x) = x2 - 4x + 1,

A: Given function: fx=x2-4x+1

Q: The domain D; and the range Rf of the function f (x) = V4 - Vx are:

A: For a function, y=f(x), the set of real values of x for which f(x) is defined is called the domain…

Q: A rectangle has a length of 16 inches and a width of 9 inches. If the length is increased by x…

A:

Q: A function f(x) is given as follows: 2x +1 f(x) = 3x - 1 f-(1) =?

A:

Q: Evaluate the function ( f + g)(−1) for f(x) = x + 3 and g(x) = x2 − 2.

A: For two functions f and g, we have, f+gx=f(x)+g(x)

Q: Let f(x) = 2x - 1 and g(x) = x2 + x - 2. Find the function: (f/g)(x).

A: Given:fx=2x-1gx=x2+x-2Formula:fgx=fxgx

Q: Evaluate the function ( f + g)(2) for f(x) = x + 3 and g(x) = x2 − 2.

A: Solution:f(x)=x+3    and     g(x)=x2-2To find (f+g)(2):Formula:(f+g)(x)=f(x)+g(x)

Q: Find the two functions f and g such that:

A:

Q: Determine the intervals upon which the given function is increasing or decreasing. f(x) = 3r + 12x?

A: The given function fx=3x3+12x2 differentiate with respect to x f'x=9x2+24x       =3x3x+8

Q: Determine where the function is concave upward and where it is concave downward. (Enter your answer…

A: Given that, The function changes concavity at the inflection point. To find inflection point, solve…

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: Let f(x) = x3 + 3, g(x) = x2 - 3, and h(x) = 3x + 3. Find the rule for the function. fgh

A: Use the rule of composite functions.

Q: Find the domain of the function using interval notation. f(x) =  1 x2 − x − 30

A: Given:     To  determine: Domain in interval notation.

Q: Find the open intervals on which the function is increasing or decreasing           f(x) = (x −…

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: Evaluate f'(a) for the function f(x)= 2x² – 5x+1 What does f'(a) represent?

A: NOTE: Refresh your page if you can't see any equations. . take derivative take x=a

Q: Let f(x) = x3 + 2, g(x) = x2 - 3, and h(x) = 4x + 10. Find the rule for the function. f-g divided…

A:

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: 8 Find the domain of the function f(x) x-7

A: Domain:- All those values of x such that f(x) exist.

Q: Consider the following function. f(x) = 4x3 – x4 (a) Make a sign diagram for the first derivative.…

A: We use second derivative test to find inflection point and by first derivative test find relative…

Q: Express the function h(x)=1x+7 in the form f∘g. If g(x)=(x+7), find the function f(x)

A: Given,

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

A: Given, hx=2x-53

Q: Consider the function f(x)=2x^2−2 for x≥0. What is the domain of f−1(x)?  answer in interval…

A: Domain set of all input values where f defined Range set of all output values

Q: What is unusual about the domain of the composite function f ◦ g for the functions f (x) = x1/2 and…

A:

Q: Let f(x) = 2x - 1 and g(x) = x2 + x - 2. Find the function: (f + g)(x)

A: Given: fx=2x-1  and gx=x2+x-2

Q: ) Determine the Range of the function g(x) = x³ for the Domain: {-1,0,1}

A:

Q: find and simplify f (a +h) -f (a) / h     (h is equal/not equal to 0) for function  F(x) =…

A: Consider the provided question,

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

A:

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: Consider the following function. f(x) = x4 - 8x3 + 18x² + 4 %3D (a) Make a sign diagram for the…

A:

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.