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

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Answer 1 · 2017-05-06T12:37:11

The answer is #[fog] (x)=25x^4-1# and #[gof] (x)=5x^4-10x^2+5#

This is a composition of functions

#f(x)=x^2-1#

#g(x)=5x^2#

#[fog] (x)=f(g(x))=f(5x^2)=(5x^2)^2-1#

#=25x^4-1#

#[gof] (x)=g(f(x))=g(x^2-1)=5(x^2-1)^2#

#=5(x^4-2x^2+1)#

#=5x^4-10x^2+5#