1
AP EAPCET 2022 - 4th July Evening Shift
+1
-0

The domain of the real valued function $$f(x)=\sin \left(\log \left(\frac{\sqrt{4-x^2}}{1-x}\right)\right.$$ is

A
$$(1,4)$$
B
$$(-1,1)$$
C
$$(-2,1)$$
D
$$(-2,4)$$
2
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

The range of the real valued function $$f(x)=\sqrt{\frac{x^2+2 x+8}{x^2+2 x+4}}$$ is

A
$$\left[\sqrt{\frac{7}{3}}, \infty\right)$$
B
$$(0, \infty)$$
C
$$(1, \infty)$$
D
$$\left(1, \sqrt{\frac{7}{3}}\right]$$
3
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

If $$f(x)=\sqrt{2-x^2}$$ and $$g(x)=\log (1-x)$$ are two real valued functions, then the domain of the function $$(f+g)(x)$$ is

A
$$[-2,2]$$
B
$$[-2,1)$$
C
$$(-\infty, 1)$$
D
$$(1,2]$$
4
AP EAPCET 2021 - 20th August Morning Shift
+1
-0

$$f(x)=\sin x+\cos x \cdot g(x)=x^2-1$$, then $$g(f(x))$$ is invertible if

A
$$\frac{-\pi}{4} \leq x \leq \frac{\pi}{4}$$
B
$$\frac{-\pi}{2} \leq x \leq 0$$
C
$$\frac{-\pi}{2} \leq x \leq \pi$$
D
$$0 \leq x \leq \frac{\pi}{2}$$
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