Find the inverse of f(x)=10+13x9,if it exists.

Question

 Find the inverse of f(x)=(10+13x)/99,if it exists.

 

Enter any noninteger coefficient as a fraction. If there is no inverse, enter "none".

f^-1(x)=

Answer 1

f(x) = (10 + 13x) / 99

 

The steps are:

 

1. Replace "f(x)" with "y" to simplify the next steps:

 

y = (10 + 13x) / 99

 

2. Switch x and y:

 

x = (10 + 13y) / 99

 

3. Solve for y:

 

x = (10 + 13y) / 99

99x = (10 + 13y)

99x - 10 = 13y

(99x - 10) / 13 = y

 

4. Substitute f^-1 (x) for y

 

(99x - 10) / 13 = f^-1 (x)

f^-1 (x) = (99x - 10) / 13 = 99/13 x - 10/13