1
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
$$0 \leq x \leq \frac{\pi}{2}$$
2
AP EAPCET 2021 - 20th August Morning Shift
+1
-0

If $$f: z \rightarrow z$$ is defined by $$f(x)=x^9-11 x^8-2 x^7+22 x^6+x^4 -12 x^3+11 x^2+x-3, \forall x \in z$$, then $$f(11)$$ is equal to

A
7
B
8
C
6
D
9
3
AP EAPCET 2021 - 20th August Morning Shift
+1
-0

Let $$f(x)=x^3$$ and $$g(x)=3^x$$, then the quadratic equation whose roots are solutions of the equation $$(f \circ g)(x)=(g \circ f)(x)$$ (for $$x \neq 0$$) is

A
$$x^2-6 x+3=0$$
B
$$x^2-6 x+9=0$$
C
$$x^2-x+3=0$$
D
$$x^2-3=0$$
4
AP EAPCET 2021 - 19th August Evening Shift
+1
-0

The real valued function $$f(x)=\frac{x}{e^x-1}+\frac{x}{2}+1$$ defined on $$R /\{0\}$$ is

A
an odd function
B
an even function
C
Both even and odd function
D
Neither even nor odd function
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