If f is one-to-one, find the equation for its inverse

Question

f(x)=√x+9 , x≥-9

 

Answer 1

As Arturo pointed out your problem needs parenthesis.

There is no need for the restriction x≥-9 unless your

function is f(x)=√(x+9)

 

f(x) = √(x+9)

replace f(x) with y

y = √(x+9) 

switch the x and y variables

x = √(y+9) 

solve for y

x² = y+9

y = x²-9

replace y with f^-1(x)

f^-1(x) = x²-9

Answer 2

WHEN YOU HAVE THIS TYPE OF QUESTION, YOU MUST HAVE BEEN TAUGHT THE GENERAL PROCESS FOR FINDING THE INVERSE, WHICH IS TO INTERCHANGE X & Y (y is f(x)), solve for the new y, and then relabel it as f^-1.

 

Can you do it now?