Question

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

Answer 1

Answer:

$\huge\boxed{f^{-1}(x)=4x+48}$

Step-by-step explanation:

In order to find the inverse of a function, we need to follow a couple of steps.

• Step 1: Write the function as $y=mx+b$
• Step 2: Swap all x and y values
• Step 3: Solve for y
• Step 4: Replace y with $f^{-1}(x)$

We can follow these steps to find the inverse of this function.

Step 1: We can just replace the f(x) with y, making our function $y=\frac{1}{4}x-12$.

Step 2: We can swap where the x and y values are, making our equation

$x = \frac{1}{4}y-12$

Step 3: We can now solve for y.

• $x = \frac{1}{4}y-12$
• $x + 12 = \frac{1}{4}x$
• $4x+48 =y$

We now have the function as $y = 4x+48$.

Step 4: We can now replace the y with $f^{-1}(x)$.

$f^{-1}(x) =4x+48$

Therefore the inverse of $f(x) = \frac{1}{4}x-12$ is $f^{-1}(x) =4x+48$.

Hope this helped!