Question

The domain for which the functions defined by f(x) = 3x² – 1 and g(x) = 3 + x are equal is ______.

Options

• `{- 1, 4/3}`

• `[-1, 4/3]`

• `(-1, 4/3)`

• `[-1, 4/3)`

Answer 1

The domain for which the functions defined by f(x) = 3x² – 1 and g(x) = 3 + x are equal is `{- 1, 4/3}`.

Explanation:

Given that: f(x) = 3x² – 1 and g(x) = 3 + x

f(x) = g(x)

⇒ 3x² – 1 = 3 + x

⇒ 3x² – x – 4 = 0

⇒ 3x² – 4x + 3x – 4 = 0

⇒ x(3x – 4) + 1(3x – 4) = 0

⇒ (x + 1)(3x – 4) = 0

⇒ x + 1 = 0 or 3x – 4 = 0

⇒ x = – 1 or x = `4/3`

∴ Domain = `{-1, 4/3}`.