Question

HELP PLEASE LOTS OF POINTS!!

Answer 1

Thus, f and g are inverse functions

Explanation:

Inverse Functions

If two functions f(x) and g(x) are inverses, then it follows that:

`f\circ g(x)=x`

Or:

`g\circ f(x)=x`

We are given

`\displaystyle f(x)=(1)/(4)x-6`

`g(x)=4x+24`

Let's test if they are inverse functions:

`f\circ g(x)=(1)/(4)(4x+24)-6`

Simplifying:

`f\circ g(x)=x+6-6=x`

Now find:

`\displaystyle g\circ f(x)=4\left((1)/(4)x-6\right)+24`

Operating:

`\displaystyle g\circ f(x)=x-24+24=x`

Thus, f and g are inverse functions