Question

Find the inverse function

Answer 1

• C)
  `f(x)=x^2-4x-1`

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Given function:

• 
  `f(x) =√(x+5) +2`

Find its inverse in steps below.

1) Substitute x with y and f(x) with x:

• 
  `x =√(y+5) +2`

2) Solve for y:

• 
  `x - 2 = √(y+5)`

• 
  `(x-2)^(2) =y + 5`

• 
  `x^2-4x+4=y+5`

• 
  `y=x^2-4x+4-5`

• 
  `y=x^2-4x-1`

Hence the inverse function is:

• 
  `f(x)=x^2-4x-1`

The matching choice is C.