F (x)=2x+7

Question

Find the inverse of function.

Answer 1

Let y = f(x).  Then y = 2x+7.

 

Switch x and y to get x = 2y + 7

 

Solve for y:  2y = x - 7

 

                   y = (x - 7)/2

 

So, f^-1(x) = (x - 7)/2 or equivalently, f^-1(x) = (1/2)x - 7/2

 

Note:  If you graph y = f(x) and y = f^-1(x), you should see that the                graph of y = f^-1(x) is the reflection of the graph of y = f(x) in the          line y = x.

 

 

Answer 2

F(x) = 2x + 7

x = 2F^-1(x) + 7              subtract 7 from both sides

x - 7 = 2F^-1(x)                divide both sides by 2

(x - 7) / 2 = F^-1(x)