Question

Let f be a function with domain [–3, 5] and let g(x) = | 3x + 4 |. Then, the domain of (fog) (x) is ______.

Options

• `(-3, 1/3)`

• `[-3, 1/3)`

• `[-3, 1/3]`

• `[-3, (-1)/3]`

Answer 1

Let f be a function with domain [–3, 5] and let g(x) = | 3x + 4 |. Then, the domain of (fog) (x) is `underlinebb([-3, 1/3]`.

Explanation:

Here, (fog) (x) = f [g(x)] = f (| 3x + 4 |)

Since, the domain of f is [–3, 5].

`\implies` –3 ≤ | 3x + 4 | ≤ 5

`\implies` | 3x + 4 | ≤ 5

`\implies` –5 ≤ 3x + 4 ≤ 5

`\implies` –9 ≤ 3x ≤ 1

`\implies` `-3 ≤ x ≤ 1/3`

∴ Domain of (fog) (x) is `[-3, 1/3]`.