If $h (x) = (f o g) (x)$ $h(x)=(fog)(x)$ , how do you determine $h (x) = {(2 x - 5)}^{2}$ $h(x)=(2x-5)^2$ and $f (x) = x^{2}$ $f(x)=x^2$ ?

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Answer 1 · 2018-01-11T15:48:40

See below.

The question is ambiguous. I am assuming you are looking for $g (x)$ $g(x)$

$h (x) = {(2 x - 5)}^{2}$ $h(x)=(2x-5)^2$

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

$:.$

$g(x)=2x-5$

If h(x)=(fog)(x)h(x)=(fog)(x)h(x)=(fog)(x), how do you determine h(x)=(2x-5)^2h(x)=(2x−5)2h(x)=(2x-5)^2 and f(x)=x^2f(x)=x2f(x)=x^2?