#### 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.

#### Solution

It is given that the functions *f*(*x*) = 3*x*^{2} − 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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Solution Find the Set of Values of X for Which the Functions F(X) = 3x2 − 1 and G(X) = 3 + X Are Equal. Concept: Functions.