Question

Write the range of the function f(x) = e^x−[x], x ∈ R.

 

Answer 1

f(x) = e^x−[x], x ∈ R

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