Find the roots of the function $y = x-2^x + 2$

Question

Given the function $ y = x-2^x + 2$, how many real roots does it have?

There are two roots, but I can only find one for analysis.

From $x+2=2^x$, if $x=2$, then $x + 2 = 2^x= 2+2=2^2 \text{ (ok)} $

Answer 1

Notice that as $x$ goes to infinity, $y$ goes to minus infinity. Also as $x$ goes to minus infinity, $y$ goes to minus infinity.

And $y$ has a maximum at one point(check the derivative). If the maximum is positive then there are two zeros. If the maximum is zero, then y has one zero.