If $h (x) = f (g (x))$ $h(x)=f(g(x))$ how do you determine f(x) and g(x) given $h (x) = 2 x^{2} - 1$ $h(x)=2x^2-1$ ?

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Answer 1 · 2018-06-21T11:34:02

There are an infinite number of valid answers; the one they're probably looking for is $f (x) = 2 x - 1$ $f(x)=2x-1$ and $g (x) = x^{2}$ $g(x)=x^2$ .

We could have also said $f (x) = x - 1, g (x) = 2 x^{2}$ $f(x)=x-1, g(x)=2x^2$ or $f (x) = x, g (x) = 2 x^{2} - 1$ $f(x)=x, g(x)=2x^2-1$ or others.

If h(x)=f(g(x))h(x)=f(g(x)) how do you determine f(x) and g(x) given h(x)=2x2−1h(x)=2x^2-1?