college algebra

Question

Find functions f and g such that ​(f◦​g)(x)=​h(x), where ​h(x)=5x+11.

Answer 1

There actually are a handful of functions f(x) and g(x) that make this work!

Anything where you can combine the function f(x) and g(x) to get f(g(x)) = 5x + 11

for example if you picked

f(x) = x and g(x) = 5x + 11 that would work

because f(g(x)) would be f(5x + 11) = 5x + 11

but similarly so would

f(x) = x + 11 and g(x) = 5x

because f(g(x)) = f(5x) = 5x + 11

so you just need to pick some combination of functions where that property would hold

I hope that helps! :)