Question

Let f: R → R be defined by f(x) = 3x 2 – 5 and g: R → R by g(x) = `x/(x^2 + 1)` Then gof is ______.

Options

• `(3x^2 - 5)/(9x^4 - 30x^2 + 26)`

• `(3x^2 - 5)/(9x^4 - 6x^2 + 26)`

• `(3x^2)/(x^4 + 2x^2 - 4)`

• `(3x^2)/(9x^4 + 30x^2 - 2`

Answer 1

Let f: R → R be defined by f(x) = 3x 2 – 5 and g: R → R by g(x) = `x/(x^2 + 1)` Then gof is `(3x^2 - 5)/(9x^4 - 30x^2 + 26)`.

Explanation:

Given that, f(x) = 3x² – 5 and g(x) = `x/(x^2 + 1)`

gof(x) = g(f(x))

= g(3x² – 5)

= `(3x^2 - 5)/((3x^2 - 5)^2 + 1)`

= `(3x^2 - 5)/(9x^4 - 30x^2 + 25 + 1)`

= `(3x^2 - 5)/(9x^4 - 30x^2 + 26)`