TS EAMCET · Maths · Functions
The function \(f: R \rightarrow R\) is defined by \(f(x)=\cos ^2 x+\sin ^4 x\) for \(x \in R\), then \(f(R)\) is equal to
- A \(\left(\frac{3}{4}, 1\right]\)
- B \(\left[\frac{3}{4}, 1\right)\)
- C \(\left[\frac{3}{4}, 1\right]\)
- D \(\left(\frac{3}{4}, 1\right)\)
Answer & Solution
Correct Answer
(C) \(\left[\frac{3}{4}, 1\right]\)
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} & f(x)=\cos ^2 x+\sin ^4 x=1-\sin ^2 x+\sin ^4 x \\ & =1-\sin ^2 x\left(1-\sin ^2 x\right)=1-\sin ^2 x \cos ^2 x \\ & =1-\frac{1}{4} \sin ^2 2 x \end{aligned} \]…
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