Question

g(x) = -x^2+1
Determine the equation of g^-1(x) algebraically and state its domain and range.

Answer 1

\[g(x)=-x^2+1\] Determine the equation of \[g^-1(x)\] algebraically and state its domain and range.

Answer 2

To do this, replace y with x
y = -x^2 + 1
x = -y^2 + 1
x - 1 = -y^2
1 - x = y^2
y = sqrt(1-x)

so the inverse of g(x) is sqrt(1-x)