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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)`
Solution
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}`.
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