Solution Found!
Find possible choices for outer and inner funct ions f a
Chapter 6, Problem 32E(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.
\(h(x)=2 /\left(x^{6}+x^{2}+1\right)^{2}\)
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.
\(h(x)=2 /\left(x^{6}+x^{2}+1\right)^{2}\)
ANSWER:Step by step solution Step 1 of 2 6 2 2 Consider a given function h(x) = 2/(x +x +1) . Now find possible ou ter (x) nd g(x) function. The function f g c°n be written a s (g(x)). Here the outer function f(x) = x2 which work 6 2 on inner function g(x) = x +x +1. Let’s check this by substituting the fu nction g (x) in the f nction f (x): 2 f(x) = x2 2 f(g(x)) = (g(x)) 2 f(g(x)) = (x +x +1)2