(a) Explanation Given: The functions are f ( x ) = x 2 + 2 x − 1 , g ( x ) = 2 x − 3 . Calculation: The composite function ( f ∘ g ) ( x ) is defined as follows. ( f ∘ g ) ( x ) = f ( g ( x ) ) = f ( 2 x − 3 ) Substitute 2 x − 3 for x in f ( x ) as follows (b) To determine The value of the function g ∘ f . (c) To determine The value of the function g ∘ g ∘ g .

Essential Calculus: Early Transcendentals

2nd Edition

ISBN: 9781133112280

Author: James Stewart

Publisher: Cengage Learning

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Question

Chapter T, Problem 7CDT

(a)

To determine

The value of the function f∘g.

(b)

To determine

The value of the function g∘f.

(c)

To determine

The value of the function g∘g∘g.

Expert Solution & Answer

Chapter T Solutions

Essential Calculus: Early Transcendentals

Ch. T - Evaluate each expression without using a...Ch. T - Simplify each expression. Write your answer...Ch. T - Expand and simplify. 3(x + 6) + 4(2x − 5) (x +...Ch. T - Factor each expression. 4x2 − 25 2x2 + 5x − 12 x3...Ch. T - Simplify the rational expression. Ch. T - Rationalize the expression and simplify. (a) (b)...Ch. T - Rewrite by completing the square. x2 + x + 1 2x2...Ch. T - Solve the equation. (Find only the real...Ch. T - Solve each inequality. Write your answer using...Ch. T - State whether each equation is true or...

Ch. T - Find an equation for the line that passes through...Ch. T - Prob. 2BDT Ch. T - Prob. 3BDT Ch. T - Let A(−7, 4) and B(5, −12) be points in the...Ch. T - Sketch the region in the xy-plane defined by the...Ch. T - The graph of a function f is given at the left....Ch. T - If f(x) = x3, evaluate the difference quotient...Ch. T - Find the domain of the function. (a)...Ch. T - How are graphs of the functions obtained from the...Ch. T - Without using a calculator, make a rough sketch of...Ch. T - Let Evaluate f(−2) and f(1). Sketch the graph of...Ch. T - Prob. 7CDT Ch. T - Prob. 1DDT Ch. T - Convert from radians to degrees. (a) 5/6 (b) 2 Ch. T - Find the length of an arc of a circle with radius...Ch. T - Find the exact values. (a) tan(/3) (b) sin(7/6)...Ch. T - Express the lengths a and b in the figure in terms...Ch. T - If sinx=13 and secy=54, where x and y lie between...Ch. T - Prove the identities. tan θ sin θ + cos θ = sec...Ch. T - Find all values of x such that sin 2x = sin x and...Ch. T - Sketch the graph of the function y = 1 + sin 2x...

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