Mathematics Let f(x) = 1/2 - ≤ft(π x/2), -1

Correct Answer is : [−12,1)≤ft[-1/2,1)[−21,1)

Correct Answer is : [−12,1)≤ft[-1/2,1)[−21,1)

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TS EAMCET 5-Aug-2021 Shift 2 Question Paper

Section: Mathematics

Question : 1 of 160

Marks: +1, -0

f(x)

\frac{1}{2} - \tan\left(\frac{\pi x}{2}\right)

-1 < x < 1

g(x)

\sqrt{3+4x-4x^{2}}

(f+g)

Solution: 👈: Video Solution

f(x)=\; \frac{1}{2} - \tan\left(\; \frac{\pi x}{2}\right), -1 < x < 1

g(x) \;\; = \sqrt{3+4x-4x^{2}}

\;\; = \sqrt{4-(2x-1)^{2}}

Domain of

f(x) \Rightarrow \frac{\pi x}{2} \neq (2n+1) \frac{\pi}{2}

x \neq 2n+1

Domain

\Rightarrow x \in (-1,1)

Domain of

g(x) \Rightarrow 4-(2x-1)^{2} \geq 0

\Rightarrow (2x-1)^{2} \leq 4

\Rightarrow -2 \leq 2x-1 \leq 2

\Rightarrow -\frac{1}{2} \leq x \leq \frac{3}{2}

Domain of

g(x) \Rightarrow x \in \left[-\frac{1}{2}, \frac{3}{2}\right]

Domain of

f(x)+g(x)

will be

\; x \in (-1,1) \cap x \in \left[-\frac{1}{2}, \frac{3}{2}\right]

\Rightarrow x \in \left[-\frac{1}{2},1\right)

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