Question

Which of the following pairs of functions are inverses of each other?

Answer 1

D.f(x)=8x³+6 and g(x)=³x-6/8

Explanation:

apex

Answer 2

The pair which are inverse of each other are:

Option: C

`f(x)=11x-4\ and\ g(x)=(x+4)/(11)`

Explanation:

Two functions f(x) and g(x) are said to be inverse of each other if:

fog(x)=gof(x)=x

i.e. the composition of two functions give identity no matter what the order is.

A)

`f(x)=(x)/(12)+15` and
`g(x)=12x-15`

Now we calculate fog(x):

`fog(x)=f(g(x))\\\\fog(x)=f(12x-15)\\\\fog(x)=(12x-15)/(12)+15\\\\fog(x)=x-(15)/(12)+15\\\\fog(x)=x-(55)/(4)\\eq x`

Hence, option: A is incorrect.

B)

`f(x)=(3)/(x)-10\ and\ g(x)=(x+10)/(2)`

Now we calculate fog(x):

`fog(x)=f(g(x))\\\\fog(x)=f((x+10)/(3))\\\\fog(x)=(3)/((x+10)/(3))-10\\\\fog(x)=(9)/(x+10)-10\\eq x`

Hence, option: B is incorrect.

D)

`f(x)=9+\sqrt[3]{x}\ and\ g(x)=9-x^3`

Now we calculate fog(x):

`fog(x)=f(g(x))\\\\fog(x)=f(9-x^3)`

`fog(x)=9+\sqrt[3]{9-x^3}\\eq x`

Hence, option: D is incorrect.

C)

`f(x)=11x-4\ and\ g(x)=(x+4)/(11)`

Now we calculate fog(x):

`fog(x)=f(g(x))\\\\fog(x)=f((x+4)/(11))`

`fog(x)=11* ((x+4)/(11))-4\\\\fog(x)=x+4-4\\\\fog(x)=x`

Similarly,

`gof(x)=g(f(x))\\\\gof(x)=g(11x-4)\\\\gof(x)=(11x-4+4)/(11)\\\\gof(x)=(11x)/(11)\\\\gof(x)=x`

Hence, option: C is the correct option.