Find the set of values for which the function

$f(x)=x+3, g(x)=3 x^{2}-1$

To find:- Set of values of $x$ for which $f(x)=g(x)$

Consider,

$f(x)=g(x)$

$f(x)=g(x)$

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

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

$3^{x^{2}}-4 x+3 x-4=0$

$x(3 x-4)+(3 x-4)=0$

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

$x=4 / 3$ or $x=-1$

The set values for which $f(x)$ and $g(x)$ have same value is $\{4 / 3,-1\}$.