find the inverse

Question

Find the inverse of the following function and graph both f and f^-1 on the same coordinate plane. 

f(x)=x^2-11 for x(greater than or equal to)0 

f^-1(x)=____. 

Answer 1

You're starting with

 

y = x² - 11

 

To find the inverse, just "swap" x and y, then solve for y. This new y will be f^-1(x)

 

x = y² - 11

 

y = sqrt[x + 11] = f^-1(x)

 

To double check that the answer is correct, we need both f(f^-1(x)) = x and f^-1(f(x)) = x to be true.

 

(sqrt[x + 11])² - 11 = x + 11 - 11 = x

 

sqrt[(x² - 11) + 11] = sqrt[x²] = x