Question

The number of real roots of the equation eˣ-1+x-2=0 is

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

Monotonic functions can have at most one real root.

Answer 1

The Correct Option is A

Define f(x)=eˣ-1+x-2. f'(x)=eˣ-1+1>0 So f(x) is strictly increasing and crosses zero only once. Hence there is exactly one real root.