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Grade 12Algebra

Find the range of f(x) = {x}^{x} (x is not an integer).
Here {x} represents the fractional part of x and ^ represents “raised to the power of” operator.

Profile image of Raghav
7 Years agoGrade 12
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1 Answer

Profile image of Aditya Gupta
7 Years ago
we know that {x} always lies in (0, 1)
so let y= {x}
now let {x}^{x}= y^y
lim y tends to 1 y^y = 1 and lim y tends to 0 y^y = 1. now let g(y)= y^y
so that g’(y)= y^y(ln(y)+1)
put this equal to zero, so that lny= – 1 or 1/e = y. so g(y)= 1/[e^(1/e)]
hence range is [1/[e^(1/e)], 1)

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