Question

Help me identify the function that are inverses of each other?

Answer 1

d)

I don't know what they mean 'to use composition', this is how I would do it.

Explanation:

swap the letters `x and y` then make `y` the subject and this is the inverse.

a) let `y=5x-3 => x=5y-3`

`x+3=5y`

`(x+3)/5=y`
`f(x)=5x-3, f^-1(x)=(x+3)/5`
so a) is not correct.

b) `y=2x^2-1 => x=2y^2-1`

`x+1=2y^2`

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

`sqrt[(x+1)/2]=y`

`f(x)=2x^2-1, f^-1(x)=sqrt[(x+1)/2]`

b) not correct

c) `y=7x+4 => x=7y+4`

`x-4=7y`

`(x-4)/7=y`
`f(x)=7x+4, f^-1(x)=(x-4)/7`
c) not correct

d) `y=x^2/4 +1 => x=y^2/4 +1`

`x-1=y^2/4`

`sqrt(x-1)=y/2`

`2sqrt(x-1)=y`

`f(x)=x^2/4 +1, f^-1(x)=2sqrt(x-1)`

d) is correct.