Question

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Answer 1

Answer:

Thus, f and g are inverse functions

Step-by-step 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

$\displaystyle f(x)=\frac{1}{4}x-6$

$g(x)=4x+24$

Let's test if they are inverse functions:

$f\circ g(x)=\frac{1}{4}(4x+24)-6$

Simplifying:

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

Now find:

$\displaystyle g\circ f(x)=4\left(\frac{1}{4}x-6\right)+24$

Operating:

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

Thus, f and g are inverse functions

Answer 2

Answer:

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Step-by-step explanation: