Question

Easy - Math - INVERSES - NEED ASAP PLEASE AND THANK YOU VERY MUCH!

Check my answers for two problems and do one for me - please and thank you! Just reassure me that they are right and if im wrong tell me what i did!

Answer 1

Part 1) No

Part 2) Option 4.
`f^(-1)(x)=-(1)/(3)x+3`

part 3)
`f^(-1)(9)=4`

Explanation:

Part 1) we have

`f(x)=8x-3`

`g(x)=(x+8)/3`

Find the inverse of f(x) and then compare with g(x)

Let

y=f(x)

`y=8x-3`

Exchange the variables x for y and y for x

`x=8y-3`

Isolate the variable y

`8y=(x+3)`

`y=(x+3)/8`

Let

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

`f^(-1)(x)=(x+3)/8`

therefore

the functions f(x) and g(x) are not inverses of each other

Part 2) we have

`f(x)=-3x+9`

Let

y=f(x)

`y=-3x+9`

Exchange the variables x for y and y for x

`x=-3y+9`

Isolate the variable y

`3y=-x+9`

`y=(-x+9)/3`

Let

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

`f^(-1)(x)=(-x+9)/3`

`f^(-1)(x)=-(1)/(3)x+3`

Part 3) we know that

For
`x=4`,
`f(x)=9`

so

For
`x=9`,
`f^(-1)(9)=4`