Question

which functions are inverses of each other?A. both pair 1 and pair 2B. pair 1 only C. Pair 2 only D. neither pair 1 nor pair 2

Answer 1

The pair one functions are given below as

`\begin{gathered} f(x)=2x-6,g(x)=(x)/(2)+3 \\ f(g(x))=2((x)/(2)+3)-6 \\ g(f(x))=(2x-6)/(2)+3 \end{gathered}`

Step 1:

From pair 1, substitute the value of x=1 in the

`\begin{gathered} f(x)=2x-6, \\ f(1)=2(1)-6 \\ f(1)=2-6 \\ f(1)=-4 \\ \\ g(x)=(x)/(2)+3 \\ g(-4)=-(4)/(2)+3 \\ g(-4)=-2+3 \\ g(-4)=1 \end{gathered}`

Step 2:

For pair 2, substitute x=1

`f(x)=7x,g(x)=-7x`
`\begin{gathered} f(x)=7x \\ f(1)=7(1) \\ f(1)=7 \\ \\ g(x)=-7x \\ g(7)=-7(7) \\ g(7)=-49 \end{gathered}`

Step 3:

From pair one,

`f(1)=-4,g(-4)=1`

From pair 2,

`f(1)=7,g(7)=-49`
`f(x)=y,g(y)=x(\text{inverse)}`

From the above conclusion, we can say that

The final answer is

PAIR 1 ONLY

OPTION B is the right answer