What is the range of xln(x) ?

The range of xln(x) is f(x)>=-1/e

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range of xln(x)

range

x ln (x)

f (x) \geq - \frac{1}{e}

Solution steps

Find the minimum and maximum value in each defined interval and unite the results

Domain of

x ln (x) : x > 0

Extreme Points of

x ln (x) :

Minimum

(\frac{1}{e}, - \frac{1}{e})

Find the range for the interval

0 < x < \infty : - \frac{1}{e} \leq f (x) < \infty

Combine the ranges of all domain intervals to obtain the function range

f (x) \geq - \frac{1}{e}

y = x^{2} + 7

f (x) = \frac{3}{x} - 3

f (x) = 2 x + 9 - 4

f (x) = \frac{3 x ^{2} - 5 x - 2}{x + 3}

f (x) = x^{2} - 1, x \leq 0