Given the function�" f(x)=1/4x− 3, find a formula for the inverse function.

change your x's to y's

y=1/4x-3
x=1/4y-3
x-3=1/4y
4(x-3)=y

you got it from there

Ah, the inverse function! It's like finding a secret code to undo all the math shenanigans. Let's tackle this one together.

To find the inverse function, we need to switch the roles of x and y. So, start by swapping the x and y in the original equation:

x = (1/4)y - 3

Now, let's isolate y and make it the subject of this crazy math equation:

4x = y - 12

Almost there! We just need to add 12 to both sides to completely free y:

4x + 12 = y

And...voila! We've just unlocked the secret formula for the inverse function: y = 4x + 12. Time to celebrate! 🎉

To find the formula for the inverse function, we need to interchange the roles of 'x' and 'f(x)' and solve for 'x'.

Let's start by getting the equation in terms of 'x' and 'f(x)':

f(x) = 1/4x - 3

Now, we'll interchange 'x' and 'f(x)':

x = 1/4f(x) - 3

Next, let's solve this equation for 'f(x)':

x + 3 = 1/4f(x)

To eliminate the fraction, we'll multiply both sides of the equation by 4:

4(x + 3) = f(x)

Expanding the left side:

4x + 12 = f(x)

Therefore, the formula for the inverse function is:

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