Question

`f : x -> sqrt((3x^2 - 1)` and `g : x -> sin (x)` then `gof : x ->`?

Options

• `sin (3x^2 - 1)`

• `sin sqrt(3x^2 - 1)`

• `sqrt(sin 3x^2 - 1)`

• `sqrt(3x^2 - 1) sin(x)`

Answer 1

`sin sqrt(3x^2 - 1)`

Explanation:

For `f : x -> sqrt(3x^2 - 1)` and `g : x -> sin x`

`f(x) = sqrt(3x^2 - 1), g(x) = sin x`

`gof (x) = g[f(x)] = g[sqrt(3x^2 - 1)]`

∴ `gof(x) = sin sqrt(3x^2 - 1)`

Hence, `gof : x -> sin sqrt(3x^2 - 1)`