inverse function help

Question

Given the function 

f(x)=  1  x - 6 find a formula for the inverse function and show work 

          5

Answer 1

Step 1:  Replace "f(x)" with "y":  y=x/5 - 6

 

Step 2:  Switch the "x" and "y":  x = y/5 - 6

 

Step 3:  Solve for y:

 

x = y/5 - 6

 

5x = y - 30    (multiply the equation by 5 to remove the fraction)

 

5x + 30 = y   (add 30 to both sides of the equation)

 

y = 5x + 30   (rewrite equation in slope-intercept form)

 

Step 4:  Replace "y" with inverse notation, f^-1(x)

 

f^-1(x) = 5x +30