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General Tips for Choosing Function

Find the set ...

Question

Find the set of values of x for which the functions $f (x) = 3 x^{2} - 1$ and $g (x) = 3 + x$ are equal.

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Solution

$∵ f (x) = g (x) \Rightarrow 3 x^{2} - 1 = 3 + x \Rightarrow 3 x^{2} - x - 4 = 0 \Rightarrow 3 x^{2} - 4 x + 3 x - 4 = 0 \Rightarrow x (3 x - 4) + 1 (3 x - 4) = 0 \Rightarrow (3 x - 4) (x + 1) = 0 ∴ x = - 1, \frac{4}{3}$

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