Question

Find functions f and g such that h = g ∘ f. (note: the answer is not unique. enter your answers as a comma-separated list of functions. use non-identity functions for f and g.) h(x) = 1 x2 − 81

Answer 1

It is given in the question that

$h(x) = (fog)(x) = x^2 -81$

And $x^2 -81$

can also be written as

$(x^2 -40) -41$

Therefore,

$(fog)(x) = (x^2 -40)-41$

$f(g(x)) = (x^2 -40)-41$

That gives,

$g(x) = x^2 -40, f(x) = x-41$