Mathematics

Mathematics

Problem

On the interval

I = [-2, 2]

, if the function

f(x) = \begin{cases} (x+1)e^{-\left(\frac{1}{|x|} + \frac{1}{x}\right)}, & x \neq 0, \\ 0, & x = 0 \end{cases}

then which of the following hold good? a.

f(x)

is continuous for all values of

x \in I

b.

f(x)

is continuous for

x \in I - \{0\}

c.

f(x)

assumes all intermediate values from

f(-2)

to

f(2)

d.

f(x)

has a maximum value equal to

3/e

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