# Find the set of values of x for which the functions f(x)

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.

$\therefore f(x)=g(x)$

$\Rightarrow 3 x^{2}-1=3+x$

$\Rightarrow 3 x^{2}-x-4=0$

$\Rightarrow(x+1)(3 x-4)=0$

$\Rightarrow x+1=0$ or $3 x-4=0$

$\Rightarrow x=-1$ or $x=\frac{4}{3}$

Hence, the set of values of $x$ for which the given functions are equal is $\left\{-1, \frac{4}{3}\right\}$.