b) h(x) - 13 — 2х - х?). c) h(x) = V3 - x 5, d) h(x) = Vx³ + 4x2 + 1.

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...
Question

Find two functions f (x) and g(x) so that h(x) = ( f o g)(x)

The image presents three mathematical expressions for the function \( h(x) \).

b) \( h(x) = |3 - 2x - x^2| \)

This expression defines the function \( h(x) \) as the absolute value of the quadratic expression \( 3 - 2x - x^2 \).

c) \( h(x) = \frac{5}{\sqrt{3-x}} \)

This expression defines the function \( h(x) \) as the fraction \( \frac{5}{\sqrt{3-x}} \), where the denominator is the square root of \( 3 - x \).

d) \( h(x) = \sqrt[5]{x^3 + 4x^2 + 1} \)

This expression defines the function \( h(x) \) as the fifth root of the polynomial \( x^3 + 4x^2 + 1 \).
Transcribed Image Text:The image presents three mathematical expressions for the function \( h(x) \). b) \( h(x) = |3 - 2x - x^2| \) This expression defines the function \( h(x) \) as the absolute value of the quadratic expression \( 3 - 2x - x^2 \). c) \( h(x) = \frac{5}{\sqrt{3-x}} \) This expression defines the function \( h(x) \) as the fraction \( \frac{5}{\sqrt{3-x}} \), where the denominator is the square root of \( 3 - x \). d) \( h(x) = \sqrt[5]{x^3 + 4x^2 + 1} \) This expression defines the function \( h(x) \) as the fifth root of the polynomial \( x^3 + 4x^2 + 1 \).
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