How to solve these?

Question

Given that f(x) = √x+2 is a one-to-one function, find the
following:

 

a. f(7)

 

 

b. f^-1(3)

 

 

Do I plug the 7 and 3 into the x in the sqrt? I don't understand.

Answer 1

a. Yes, you plug in 7 in place of x and solve the square root.

 

b. f^-1(x) is the inverse function of f(x), which you, first, need to find out, before plugging in x=3

 

A detailed description of how to find the inverse function can be found online, including here:

http://www.coolmath.com/algebra/16-inverse-functions/05-how-to-find-the-inverse-of-a-function-01

 

f(x) = √(x+2)

We follow the following 4 steps to find the inverse function f^-1(x)

Step 1: change f(x) to y

       y = √(x+2)

Step 2: switch x and y

       x = √(y+2)
Step 3: solve for y

      we square both sides

      x² = y+2

      y = x²-2

Step 4: Change y to inverse notation f^-1(x)

      f^-1(x) = x²-2

 

Now, you plug in x=3, to get

      f^-1(3) = 3²-2 = 7