Find the inverse of each of the given functions. f(x) = 4x - 12

Solution:

An inverse function reverses the operation done by a particular function. In other words, the inverse function undoes the action of the other function.

Given, f(x) = 4x - 12

First replace f(x) with y.

y = 4x - 12

Next replace x with y and y with x.

x = 4y - 12

Solving for y, we get,

4y = x + 12

y = (x + 12)/4

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

f ^-1(x) = (x + 12)/4

Verification:

(f∘f ^-1)(x)= x

(f∘f ^-1) (x)= f [f ^-1(x)]

= f [(x + 12)/4]

= f [x/4 + 12/4]

= 4[x/4 + 12/4] - 12

= x + 12 - 12

= x

Therefore, the inverse function is f ^-1(x) = (x + 12)/4

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Find the inverse of each of the given functions. f(x) = 4x - 12

Summary:

Given the function f(x) = 4x - 12, the inverse function is f ^-1(x) = (x + 12)/4.