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Question
Find the values of x for which the functions f(x) = 3x2 – 1 and g(x) = 3 + x are equal.
Solution
f and g functions defined by f(x) = 3x2 – 1 and g(x) = 3 + x
For what real numbers x, f(x) = g (x)
To satisfy the condition f(x) = g(x)
Should also satisfy
3x2 – 1 = 3 + x
⇒ 3x2 – x – 3 – 1 = 0
⇒ 3x2 – x – 4 = 0
Splitting the middle term,
We get,
⇒ 3x2 + 3x – 4x – 4 = 0
⇒ 3x(x + 1) – 4(x + 1) = 0
⇒ (3x – 4)(x + 1) = 0
⇒ 3x – 4 = 0 or x + 1 = 0
⇒ 3x = 4 or x = –1
⇒ x = `4/3`, –1
Hence, for x = `4/3`, –1, f(x) = g(x)
i.e., Given functions are equal.
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