Question

Which pair of functions are inverses of each other?1+6A. f(x) = - 6 and g(x) =B. f(x) = { + 4 and g(x) = 3x - 4C. f(x) = 2x– 9 and g(x) = $49D. f(x) = { and g(x) = 5x3

Answer 1

To know if a pair of functions are inverses of each other we must verify if

$(f\circ g)(x)=(g\circ f)(x)=x$

Option A.

$f(x)=\frac{2}{x}\text{ and }g(x)=\frac{x+6}{2}$

Then

$\begin{gathered} (f\circ g)(x)=f(g(x)) \\ =\frac{2}{\frac{x+6}{2}}=\frac{4}{x+6} \end{gathered}$

So, option A is not the correct answer.

Option B.

$f(x)=\frac{x}{3}+4\text{ and}g(x)=3x-4$

Then

$\begin{gathered} (f\circ g)(x)=f(g(x)) \\ =\frac{3x-4}{3}+4 \\ =x-\frac{4}{3}+4 \\ =x+\frac{8}{3} \end{gathered}$

So, option B is not the correct answer.

Option C.

$f(x)=2x-9\text{ and }g(x)=\frac{x+9}{2}$

Then

$\begin{gathered} (f\circ g)(x)=f(g(x)) \\ =2(\frac{x+9}{2})-9 \\ =x+9-9 \\ =x \end{gathered}$

And

$\begin{gathered} (g\circ f)(x)=g(f(x)) \\ =\frac{2x-9+9}{2} \\ =\frac{2x}{2} \\ =x \end{gathered}$

Finally, we can see that option C meets the condition.

So, the answer is letter C.