Question

Which of the following functions satisfies the following conditions: f is increasing and has an x intercept at x=0?

a. (e^x)+2
b.2-(2e^x)
c.2-(e^-x)
d.(-e^-x)
e.(e^2x)-1

Answer 1

It's option e. (e^2x) is an increasing function as it has a positive slope. And to get the x-intercept, put y = 0 and solve for x. It will be:
y = (e^2x) - 1
0 = (e^2x) - 1
e^2x = 1
2x = ln (1)
x = 0 (because ln (1) = 0) so that means the x-intercept is 0.