find the inverse

Question

INVERSE of f(x)  5x-1/3

Answer 1

Hi Tammy,

 

To find an inverse, you can always follow a certain process each time, and it goes like this.

 

Write y = 5x - 1/3

 

Now solve for x as a function of y.

 

5x = y + 1/3

 

x = y/5 + 1/15

 

Now, switch variables. What you call x, call y and vice versa. So,

 

y = x/5 + 1/15

 

Now, call y f^-1(x).

 

f^-1(x) = x/5 + 1/15

 

You can always check yourself to see if you are correct. You should be able to write f(f^-1(x)) = x.

 

f(f^-1(x)) = 5f^-1(x) - 1/3 = 5(x/5 + 1/15) - 1/3 = x + 1/3 - 1/3 = x  Check

Answer 2

INVERSE of f(x) =  5x-1/3

 

to find the inverse of a function there are steps to follow:

 

1)  replace f(x) with y

     y = 5x - 1/3

 

2) swap x and y within the function

    x = 5y - 1/3

 

3) solve for y

    5y = x + 1/3

     y = x/5 + 1/15

 

4) replace y with f^-1(x)

 

    f^-1(x) = x/5 + 1/15