Question

For f(x) =1/x^2-3

find:

(a) f(3) (3 points)

(b) f(2+h) (3 points)

Answer 1

`f(3) = (-26)/(9)`

`f(2 + h) = (- 11 - 12h - 12^2)/(4 + 4h + h^2)`

Explanation:

Given

`f(x) = (1)/(x^2) - 3`

Required

Find f(3) and f(2 + h)

Solving f(3)

Substitute 3 for x in
`f(x) = (1)/(x^2) - 3`

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

`f(3) = (1)/(9) - 3`

Take LCM

`f(3) = (1 - 27)/(9)`

`f(3) = (-26)/(9)`

Solving f(2 + h)

Substitute 2 + h for x in
`f(x) = (1)/(x^2) - 3`

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

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

`f(2 + h) = (1)/(4 + 2h + 2h + h^2) - 3`

`f(2 + h) = (1)/(4 + 4h + h^2) - 3`

Take LCM

`f(2 + h) = (1- 3(4 + 4h + h^2))/(4 + 4h + h^2)`

`f(2 + h) = (1- 12 - 12h - 12^2)/(4 + 4h + h^2)`

`f(2 + h) = (- 11 - 12h - 12^2)/(4 + 4h + h^2)`