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 .......

Question

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 ......., $[0,1]$, $[0, \infty)$, $[0,1)$, $\left[0, \frac{1}{2020}\right)$

MARKS App · Accepted Answer

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.

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