Answer
$\frac{1±\sqrt 5}{2}$
Work Step by Step
when x $\lt$ a
f(x) =x+1 is continous (basic function)
when x $\gt$ a
f(x)=$x^{2}$ is also continous (basic function)
at x=a, we have
$\lim\limits_{x \to a^{-}}$ f(x)= a+1
$\lim\limits_{x \to a^{+}}$ f(x)=$a^{2}$
To make f contiunous at x=a
$\lim\limits_{x\to a^{-}}$ f(x) = $\lim\limits_{x \to a^{+}}$ f(x)
a+1=$a^{2}$
a=$\frac{1±\sqrt 5}{2}$
