If \(f: \mathbf{R} \rightarrow \mathbf{R}\) is defined as \(f(x)=\frac{x^6}{x^6+2020}\), \(\forall x \in…
If \(f: \mathbf{R} \rightarrow \mathbf{R}\) is defined as \(f(x)=\frac{x^6}{x^6+2020}\), \(\forall x \in \mathbf{R}\), then the range of \(f\) is .......
\([0,1]\)
\([0, \infty)\)
\([0,1)\)
\(\left[0, \frac{1}{2020}\right)\)
Solution
We have,
\(\begin{aligned}
& \quad x^6+2020 > x^6 \\
& \Rightarrow \frac{x^6}{x^6+2020} < 1 \\
& \therefore \text { Range }=[0,1)
\end{aligned}\)
Hence, option (c) is correct.