Question

Which functions are inverses of each other?a. Both Pair 1 and Pair 2b. Pair 1 onlyc. Pair 2 onlyd. neither Pair 1 nor Pair 2

Answer 1

For pair 1

`\begin{gathered} f(x)=2x-6,g(x)=(x)/(2)+3 \\ \mathrm{A\: function\: g\: is\: the\: inverse\: of\: function\: f\: if\: for}\: y=f\mleft(x\mright),\: \: x=g\mleft(y\mright)\: \end{gathered}`
`\begin{gathered} f(x)=2x-6 \\ f(x)=y \\ y=2x-6 \\ x=2y-6 \\ x+6=2y \\ \text{divide both side by 2} \\ (x+6)/(2)=(2y)/(2)_{} \\ y=(x)/(2)+3 \end{gathered}`

They are inverse of each other

For pair 2

`\begin{gathered} f(x)=7x,g(x)=-7x \\ \text{Inverse of f(x) = x/7} \end{gathered}`
`\begin{gathered} f(x)=7x \\ y=7x \\ x=7y \\ y=(x)/(7) \end{gathered}`

They are not inverse of each other

Therefore only pair 1 are inverse of each other

Hence the correct answer is Option B