What is the inverse of f of x equals 4x plus 12?

Answer 1

f(x) = 4x + 12

Let 'y' = f(x)

Hence

y = 4x + 12

y - 12 = 4x

x = ( y - 12) / 4

'Swop the letters'

y = ( x - 12) / 4

Hence f'(x) = ( x -12) / 4

The inverse function.

Answer 2

If f(x) = 4x + 12, to find the inverse, reverse the actions of the elements of the function in "reverse" order.

The last thing done is "+ 12", so reverse that first by "- 12"

The previous thing done was "× 4n, so reverse that by "÷ 4", but note that the divide takes precedence over subtract, so the previous step needs to be in brackets.

Thus if the inverse of f(x) is g(x), g(x) = (x - 12) ÷ 4