Question

What is the inverse of the function f(x) = 1/4x – 12?

Answer 1

To answer this, you want to start by changing 'f(x)' to 'x', and 'x' to the inverse function - let's call it 'g(x)'. This is inverting the function - it's like swapping the x and y axes around. That will give you: x = 1/4g(x) - 12

Now you want to rearrange that equation to put g(x) on the left hand side. That's not so hard to do - although I'm not sure if the question is (1/4)x or 1/(4x), so I'll answer for both:

x + 12 = (1/4)g(x)
4x + 48 = g(x)
g(x) = 4x + 48

or, if the question is 1/(4x):
x + 12 = 1/(4g(x))
1/(x + 12) = 4g(x)
1/(4x + 48) = g(x)
g(x) = 1/(4x + 48)

Answer 2

to find the inverse all you do is swap your x and y then solve it through. for this one you gotta take f(x) and make it y

y = 1/4x - 12

then swap

x = 1/4y - 12

then solve it through

x - 12 = 1/4y

divide by (1/4)

and (x - 12)4 = y should be your answer