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Question
Write the range of the function f(x) = ex−[x], x ∈ R.
Solution
f(x) = ex−[x], x ∈ R
\[\text { We know that x - [x] = {x}, which is the fractional part of any number x .} \]
\[\text{ Thus} , f(x) = e^{{x}} \]
\[\text{ Also} , 0 \leq {x} < 1\]
\[ \Rightarrow e^0 \leq e^{{x}} < e^1 \]
\[ \Rightarrow 1 \leq f(x) < e\]
\[\text{ Thus range of f(x) is } [1, e) . \]
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