Solution Found!
Find possible choices for outer and inner functions f and
Chapter 6, Problem 34E(choose chapter or problem)
31-34. Working with composite functions Find possible choices for outer and inner functions f and g such that the given function h equals \(f\ \circ\ g\). Give the domain of h.
\(h(x)=\frac{1}{\sqrt{x^{3}-1}}\)
Questions & Answers
QUESTION:
31-34. Working with composite functions Find possible choices for outer and inner functions f and g such that the given function h equals \(f\ \circ\ g\). Give the domain of h.
\(h(x)=\frac{1}{\sqrt{x^{3}-1}}\)
ANSWER:Step by step solution Step 1 of 2 Consider a given function h(x) = 1 . x 1 Now find possible outer f(x) and g(x) function. The function f g °an be written as f(g(x)). Here the outer function f(x) = 1x which work on inner function g(x) = x 1. Let’s check this by substituting the function g(x) in the function f(x): 1 f(x) = x 1 f(g(x)) = g(x) f(g(x)) = 1 x 1