How would you write the inverse function of f(x) ?

Given the function f(x), we want to find the inverse function, given by f^-1(x).

Step 1. Replace f(x) with y.

Step 2. Replace every x with a y, and every y with an x.

Step 3. Solve the equation from Step 2 for y.

Step 4. Replace y with f^-1(x).

Step 5. Verify your answer by checking that:

(f o f⁻¹)(x) = x AND (f^-1 o f)(x) = x

Example: Find the inverse function of f(x) = 3x-2.

(1) First, let's replace f(x) with y: y = 3x-2

(2) Then, let's replace all x's with y, and all y's with x: x = 3y-2

(3) Now, let's solve the equation for y: x = 3y-2

3y = x+2

y = (x+2)/3

(4) Finally, let's replace y with f^-1(x): f^-1(x) = (x+2)/3

(5) Don't forget to check your answer is correct!

x -> f(x) -> f^-1(x) gives us: ((3x-2)+2) / 3

= 3x/3

= x check complete

x > f^-1(x) -> f(x) gives us: 3((x+2)/3) -2

= (3x+6)/3 -2

= x+2-2

= x check complete