Question

Which two functions are inverses of each other?

f(x)= x, g(x) = -x
f(x)= 2x, g(x) = - 1/2x
f(x) = 4x, g(x) = 1/4x
f(x) = -8x, g(x) = 8x

Answer 1

C on edge

Explanation:

I took the test

Answer 2

Option 3 - f(x)= 4x,
`g(x) = (1)/(4)x`

Explanation:

To find : Which two functions are inverses of each other?

Solution :

Two functions are inverse if
`f(g(x))=x=g(f(x))`

Now, we find one by one

1) f(x)= x, g(x) = -x

`f(g(x))=f(-x)=-x\\eq x`

Not true.

2) f(x)= 2x,
`g(x) = -(1)/(2)x`

`f(g(x))=f(-(1)/(2)x)=2*(-(1)/(2)x)=-x\\eq x`

Not true.

3) f(x)= 4x,
`g(x) = (1)/(4)x`

`f(g(x))=f((1)/(4)x)=4*((1)/(4)x)=x`

`g(f(x))=f(4x)=(1)/(4)* 4x=x`

i.e.
`f(g(x))=x=g(f(x))` is true.

So, These two functions are inverse of each other.

4) f(x)= -8x,
`g(x) =8x`

`f(g(x))=f(8x)=8*(-8x)=-64x\\eq x`

Not true.

Therefore, Option 3 is correct.