Let `f(x)={{:((e^(x)-1)/(x)",",xgt0),(0",",x=0):}` be a real valued function.
Which one of the following statements is correct?

Options

A. f(x) is a strictly decreasing function in (0,x),
B. f(x) is a strictly increasing function in (0,x),
C. f(x) is neither increasing nor decreasing in (0,x)
D. f(x) is not decreasing in (0,x).

Answer

B

Explanation

`f(x)=(e^(x)-1)/(x)gt0`
`impliesf'(x)=(xe^(x)-(e^(x)-1))/(x^(2))=(e^(x)(x-1)+1)/(x^(2))`
`=((e^(x)(x-1))/(x^(2))+(1)/(x^(2)))`, which is a strictly increasing function.