Question

Please help me with the math question In the picture below, Thank you!

Answer 1

`f^(-1)` (6) = 12

Explanation:

given

f(x) =
`√(3x)`

to find the inverse function
`f^(-1)` (x)

let y = f(x) and rearrange making x the subject

y =
`√(3x)` ( square both sides )

y² = (
`√(3x)` )² = 3x ( divide both sides by 3 )

`(1)/(3)` y² = x

now, change y back into terms of x, with x =
`f^(-1)` (x)

`f^(-1)` (x) =
`(1)/(3)` x² , then

`f^(-1)` (6) =
`(1)/(3)` × 6² =
`(1)/(3)` × 36 = 12