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Question
Find the set of values of x for which the functions f(x) = 3x2 − 1 and g(x) = 3 + x are equal.
Solution
It is given that the functions f(x) = 3x2 − 1 and g(x) = 3 + x are equal.
\[\therefore f\left( x \right) = g\left( x \right)\]
\[ \Rightarrow 3 x^2 - 1 = 3 + x\]
\[ \Rightarrow 3 x^2 - x - 4 = 0\]
\[ \Rightarrow \left( x + 1 \right)\left( 3x - 4 \right) = 0\]
\[\Rightarrow x + 1 = 0 \text{ or } 3x - 4 = 0\]
\[ \Rightarrow x = - 1 \text{ or } x = \frac{4}{3}\]
Hence, the set of values of x for which the given functions are equal is \[\left\{ - 1, \frac{4}{3} \right\}\] .
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