How do i solve this equation without graphing on a computer or calculator:

(e^x)+x-2=0

?

This equation appears on GRE 0568, #4)

Thanks.

## GRE 0568 #4)

### Re: GRE 0568 #4)

Consider continuous function

f(x) = exp(x) + x - 2.

Its derivative is always positive. Hence, the function is monotonous, increasing and, as result, might have only one root. Secondly,

f(0) = -1 < 0;

f(1) = e - 1 > 0.

Hence, its only root is inside interval [0, 1].

f(x) = exp(x) + x - 2.

Its derivative is always positive. Hence, the function is monotonous, increasing and, as result, might have only one root. Secondly,

f(0) = -1 < 0;

f(1) = e - 1 > 0.

Hence, its only root is inside interval [0, 1].