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2. Find (fo g)(x), (g o f)(x) and the domain of each new function. a. Let f (x) = 4x² – x + 10 g(x) = 2x – 7 b. Let f (x) = Vx g(x) = 2 - 3x g(x) = 4 c. Let f (x) %3D 1- 5x d. Does (f • g)(x) always equal (g o f)(x)? When will (f • g)(x) = (g o f)(x)?

2. Find (fo g)(x), (g o f)(x) and the domain of each new function. a. Let f (x) = 4x² – x + 10 g(x) = 2x – 7 b. Let f (x) = Vx g(x) = 2 - 3x g(x) = 4 c. Let f (x) %3D 1- 5x d. Does (f • g)(x) always equal (g o f)(x)? When will (f • g)(x) = (g o f)(x)?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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2. Find \((f \circ g)(x)\), \((g \circ f)(x)\) and the domain of each new function. a. Let \(f(x) = 4x^2 - x + 10\) and \(g(x) = 2x - 7\) b. Let \(f(x) = \sqrt{x}\) and \(g(x) = 2 - 3x\) c. Let \(f(x) = \frac{4}{1 - 5x}\) and \(g(x) = \frac{1}{x}\) d. Does \((f \circ g)(x)\) always equal \((g \circ f)(x)\)? When will \((f \circ g)(x) = (g \circ f)(x)\)?
Transcribed Image Text:2. Find \((f \circ g)(x)\), \((g \circ f)(x)\) and the domain of each new function. a. Let \(f(x) = 4x^2 - x + 10\) and \(g(x) = 2x - 7\) b. Let \(f(x) = \sqrt{x}\) and \(g(x) = 2 - 3x\) c. Let \(f(x) = \frac{4}{1 - 5x}\) and \(g(x) = \frac{1}{x}\) d. Does \((f \circ g)(x)\) always equal \((g \circ f)(x)\)? When will \((f \circ g)(x) = (g \circ f)(x)\)?
Expert Solution
Step 1

Here,

we have given some functions and we have to find composite function and domain of these functions 

so,

COMPOSITE FUNCTION - Composite function are the operations applied on functions where two functions say f(x) and                                                g(x) generate a new function say h(x) , in such a way that 

                                             h(x)= g(f(x)) 

                                             so basically a function is applied to the result of another function.

 

DOMAIN - Domain are the set of all values over which a function is defined.

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