Question

If g(x)is the inverse of f(x)andf(x)=4x+12,what is g(x)?

Answer 1

To find the inverse of a function, stick a y for the f(x).

So, f(x) = 4x + 12 becomes y = 4x + 12

Then switch the x and y.

So, y = 4x + 12 becomes x = 4y + 12

Then solve for y.

x = 4y + 12
x - 4y = 12 <-- Subtract both sides by 4y
-4y = 12 - x <-- Subtract both sides by x

y = $-3 + \frac{x}{4}$

So, the inverse of f(x) is g(x) = -3 + x/4.