Use switch and solve to find f-1(x)

Question

Use switch and solve to find f-1(x)

 

F(x)= the square root of x-4

Answer 1

f(x) = (x-4)^1/2

 

y = (x-4)^1/2

 

Switch the x's and y's, solve for the new y:

 

x = (y-4)^1/2

 

x² = y-4            [Square both sides to get rid of the square root]

 

x²+4 = y = f^-1(x)

 

Check:

 

f(f^-1(x)) = (f^-1(x)-4)^1/2 = (x²+4-4)^1/2 = (x²)^1/2 = x         Check!