Find the set of values for which the function

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

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

Consider,

$f(x)=g(x)$

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

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

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

$2 x(x+2)-(x+2)=0$

$(x+2)(2 x-1)=0$

$x=-2$ or $x=$ \gg

The set values for which $f(x)$ and $g(x)$ have same value is $\{-2$, \diamond $\}$.