Question

Find p(p^-1(x)) when p(x)=x^2-4

I tried solving this and I got x^4-x+20 but that has no solution so I'm a little confused.

Answer 1

for any function p, p(p^-1(x)) = p^-1(p(x)) = x
That's what inverse does!

p(x) = x^2-4
p^-1(x) = √(x+4)

so, p(p^-1) = (p^-1)^2-4 = (√(x+4))^2-4 = x+4-4 = x
p^-1(p) = √(p+4) = √(x^2-4+4) = √x^2 = x

now, you do have to watch out and beware of the fact that the domain of p^-1 is restricted.

Answer 2

Ohh okay got it thank you!