f: \mathbb{R} \to \mathbb{R} is a function defined by f(x)=\frac{1}{e^x+2 e^{-x}} Assertion (A): f(c)=\frac{1}{3} for some values of c \in R Reason ( {\R}): 0< f(x) \leq {1}/{2 \sqrt{2}} for all x \in R Then which of the following options is correct? [TG EAPCET 12 May 2023 Shift 2]

Correct Answer is : (A) and (R) are true. (R) is the correct explanation of (A)

(A) and (R) are true. (R) is the correct explanation of (A)

(A) and (R) are true, but (R) is not the correct explanation for (A)

TS EAMCET Engineering 12 May 2023 Shift 2 Solved Paper

Section: Mathematics

Question : 69 of 160

Marks: +1, -0

f:ℝ→ℝ is a function defined by f(x)=‌

ex+2e−x

Assertion (A): f(c)=‌

for some values of c∈R
Reason (R):0<f(x)≤‌

2√2

for all x∈R
Then which of the following options is correct?

[TG EAPCET 12 May 2023 Shift 2]

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