Inverse Functions:

The inverse of a function f(x) is another function, f^-1(x), which reverses f(x).

First you should write out the equation x=f(y) (which is the same as f(x), just with y’s instead of x’s.

Then you should rearrange the equation to make y the subject.

Finally, replace y with f^-1(x).

Example 1:

If f(x) = 12 + x / 3, find f^-1(x)

x = 12 + y / 3

3x = 12 + y

y = 3x - 12

f^-1(x) = 3x - 12

Example 2:

If f(x) = 3 / 2x+5, show that ff^-1(x) = x

Inverse function - f^-1 = 3/2x - 5/2

Substitute f^-1(x) into f(x)

ff^-1(x) = 3/2(3/2x - 5/2)+5

= 3/(3/x - 5 +5)

= 3/(3/x)

= 3 x x/3

= x

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