Let $f(x) = \frac{1}{2} - an\left( \frac{\pi x}{2} ight)$, $- 1

Question

Let $f(x) = \frac{1}{2} - 	an\left( \frac{\pi x}{2} ight)$, $- 1 < x < 1$ and $g(x) = \sqrt{3 + 4x - 4x^{2}}$, then dom $(f + g)$ is given by

Dr. Abubacker · Accepted Answer

(c)
Given, $f(x) = \frac{1}{2} - 	an{\left( \frac{\pi x}{2} ight),\  - 1 < x < 1}$
Given, domain of $f(x)$ is $d_{1} = ( - 1,\ 1)$
For domain of $g(x),\ 3 + 4x - 4x^{2} \geq 0$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ (2x - 3)(2x + 1) \leq 0$
$	herefore$ Domain of $g(x)$ is $d_{2} = \left\lbrack - \frac{1}{2},\ \frac{3}{2} ightbrack$
Hence, domain of $(f + g) = d_{1} \cap d_{2} = \left\lbrack - \frac{1}{2},\ 1 ightbrack$

Q. Let $f(x) = \frac{1}{2} - \tan\left( \frac{\pi x}{2} \right)$, $- 1 < x < 1$ and $g(x) = \sqrt{3 + 4x - 4x^{2}}$, then dom $(f + g)$ is given by

Explanation

Reviewed by Dr. Abubacker

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