QuestionJune 17, 2025

if h(x)=((16+x^7)/(16-x^7))^2 find functions f(x) and g(x) so h(x)=f(g(x)) f(x)= square g(x)= square

if h(x)=((16+x^7)/(16-x^7))^2 find functions f(x) and g(x) so h(x)=f(g(x)) f(x)= square g(x)= square
if h(x)=((16+x^7)/(16-x^7))^2 find functions f(x) and g(x) so h(x)=f(g(x))
f(x)= square 
g(x)= square

Solution
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Answer

\( f(x) = x^2 \) ### \( g(x) = \frac{16 + x^7}{16 - x^7} \) Explanation 1. Identify the inner function ( g(x) ) Recognize that the expression inside the square is a candidate for ( g(x) ). Set \( g(x) = \frac{16 + x^7}{16 - x^7} \). 2. Identify the outer function ( f(x) ) The outer function ( f(x) ) takes the form of squaring its input. Thus, set \( f(x) = x^2 \).

Explanation

1. Identify the inner function ( g(x) )<br /> Recognize that the expression inside the square is a candidate for ( g(x) ). Set \( g(x) = \frac{16 + x^7}{16 - x^7} \).<br /><br />2. Identify the outer function ( f(x) )<br /> The outer function ( f(x) ) takes the form of squaring its input. Thus, set \( f(x) = x^2 \).
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