Hello!
The answer is:
The first option,
[tex]f^{-1}(x)=\frac{x-2}{4}[/tex]
Why?
To find the inverse of a function, we need to rewrite the variable "x" with "y" and the variable "y" with "x", and then, isolate "y".
We are given the function:
[tex]f(x)=4x+2[/tex]
Write "f(x)" is equal to write "y", so:
[tex]y=4x+2[/tex]
Now, finding the inverse, we have:
[tex]y=4x+2\\x=4y+2\\x-2=4y\\y=\frac{x-2}{4}[/tex]
Hence, we have that the answer is the first option,
[tex]f^{-1}(x)=\frac{x-2}{4}[/tex]
Have a nice day!
