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`