Question

Find the inverse please!

Answer 1

`\tt f^(-1)(x) =\boxed{(( x+5)/(6))^2-8}`

Explanation:

Given:

`\tt f(x) = 6 √(x+8) -5` where x ≥ -8.

To find:

`\tt f^(-1)(x)`

Solution:

let

f(x)= y

`\tt y = 6 √(x+8) -5`

Interchanging the role of x and y, we get

`\tt x = 6 √(y+8) -5`

solving for y

`\tt x+5 = 6√(y+8)`

dividing both side by 6

`\tt √(y+8)=( x+5)/(6)`

squaring both side

`\tt y+8=(( x+5)/(6))^2`

subtracting both side by 8

`\tt y=(( x+5)/(6))^2-8`

Therefore,
`\tt f^(-1)(x) =(( x+5)/(6))^2-8`