The domain for which the functions f(x)

f(x) = 3x2 − 1

g(x) = 3 + x

Given:-   f(x) = g(x) 

i.e 3x2 − 1 = 3 + x

3x2 − x − 1 − 3 = 0

3x2 − x − 4 = 0

3x2 + 3x − 4x − 4 = 0

3x(x + 1) − 4 (x + 1) = 0

(3x − 4) (x + 1) = 0

i.e $x=\frac{4}{3}$ or $x=-1$

$\therefore$ Domain for which $f(x)$ and $g(x)$ are equal is $\left\{-1, \frac{4}{3}\right\}$