Question

Find the inverse of f(ℎ) =ℎ^2 − 2ℎ + 4

ℎ ≥ 1

Answer 1

`f^(-1)`(h) =
`√(h - 1)` + 1.

Explanation:

Given, f(h) =
`h^(2)` - 2h + 4.

h ≥ 1 .

f(h) =
`(h-1)^(2)` + 3.

Now, to calculate the inverse of the function we have to interchange h and f(h). {Where interchanged f(h) will represent inverse of the function}

So,

h =
`(f(h)-1)^(2)` + 3

h - 3 =
`(f(h)-1)^(2)`

f(h) -1 =
`√(h - 1)`

f(h) =
`√(h - 1)` + 1.

f(h) ⇒ Representing inverse of f(h) as stated above.

Thus,
`f^(-1)`(h) =
`√(h - 1)` + 1.