Question

Which pairs of functions are inverses of each other?
Choose all that are correct.

Answer 1

its the second and third one

Answer 2

C and D

Explanation:

We have to find pairs of functions which are inverses of each other.

1.
`f(x)=2x+3` and
`g(x)=0.5x-3`

Suppose y=f(x)

`y=2x+3`

`2x=y-3`

`x=(y-3)/(2)`

`x=f^(-1)(y)`

`f^(-1)(y)=(y-3)/(2)`

y replace by x

Then , we get

`f^(-1)(x)=\frac[x-3}{2}`

Hence, f(x) and g(x) are not inverses to each other.

B.
`f(x)=(1)/(6)x-2`, and
`g(x)=6x-12`

Suppose,
`y=f(x)=(1)/(6)x-2`

`y+2=(1)/(6)x`

`6y+12=x`

Therefore,
`f^(-1)(x)=6x+12`

Hence, f(x) and g(x) are not inverses to each other.

C.
`f(x)=(1)/(3)x+5` and
`g(x)=3x-15`

Suppose ,
`y=f(x)=(1)/(3)x+5`

`y-5=(1)/(3)x`

`3y-15=x`

Therefore,
`f^(-1)(x)=3x-15=g(x)`

Hence, f(x) and g(x) are inverses of each other.

D.
`f(x)=x^2+7` and
`g(x)=\pm √(x-7)`

Suppose ,
`y=f(x)=x^2+7`

`y-7=x^2`

`x=\pm √(x-7)`

Therefore,
`f^(-1)(x)=\pm√(x-7)=g(x)`

Hence, f(x) and g(x) are inverses to each other.