How do you find $[f o g] (x)$ $[fog](x)$ and $[g o f] (x)$ $[gof](x)$ given $f (x) = x^{2} - 1$ $f(x)=x^2-1$ and $g (x) = 5 x^{2}$ $g(x)=5x^2$ ?

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Answer 1 · 2017-05-06T12:37:11

The answer is $[f o g] (x) = 25 x^{4} - 1$ $[fog] (x)=25x^4-1$ and $[g o f] (x) = 5 x^{4} - 10 x^{2} + 5$ $[gof] (x)=5x^4-10x^2+5$

This is a composition of functions

$f (x) = x^{2} - 1$ $f(x)=x^2-1$

$g (x) = 5 x^{2}$ $g(x)=5x^2$

$[f o g] (x) = f (g (x)) = f (5 x^{2}) = {(5 x^{2})}^{2} - 1$ $[fog] (x)=f(g(x))=f(5x^2)=(5x^2)^2-1$

$= 25 x^{4} - 1$ $=25x^4-1$

$[g o f] (x) = g (f (x)) = g (x^{2} - 1) = 5 {(x^{2} - 1)}^{2}$ $[gof] (x)=g(f(x))=g(x^2-1)=5(x^2-1)^2$

$= 5 (x^{4} - 2 x^{2} + 1)$ $=5(x^4-2x^2+1)$

$= 5 x^{4} - 10 x^{2} + 5$ $=5x^4-10x^2+5$

How do you find [fog](x)[fog](x) and [gof](x)[gof](x) given f(x)=x2−1f(x)=x^2-1 and g(x)=5x2g(x)=5x^2?