Question

Find the set of values of x for which the functions f(x) = 3x² − 1 and g(x) = 3 + x are equal.

Answer 1

It is given that the functions f(x) = 3x² − 1 and g(x) = 3 + x are equal.

$$\therefore f\left(x\right)=g\left(x\right)$$
$$\Rightarrow 3x^2-1=3+x$$
$$\Rightarrow 3x^2-x-4=0$$
$$\Rightarrow (x+1)(3x-4)=0$$

$$\Rightarrow x+1=0\text{ or }3x-4=0$$
$$\Rightarrow x=-1\text{ or }x=\frac{4}{3}$$

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