Functions · Mathematics · AP EAPCET

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MCQ (Single Correct Answer)

1
If $A \subseteq Z$ and the function $f: A \rightarrow R$ is defined by $f(x)=\frac{1}{\sqrt{64-(0.5)^{24+x-x^2}}}$, then the sum of all absolute value of elements of $A$ is
AP EAPCET 2024 - 23th May Morning Shift
2

Which of the following function are odd?

I. $f(x)=x\left(\frac{e^x-1}{e^x+1}\right)$

II. $f(x)=k^x+k^{-x}+\cos x$

III. $f(x)=\log \left(x+\sqrt{x^2+1}\right)$

AP EAPCET 2024 - 23th May Morning Shift
3
The range of the real valued function $f(x)=\frac{15}{3 \sin x+4 \cos x+10}$ is
AP EAPCET 2024 - 22th May Evening Shift
4

Define the function, $f, g$ and $h$ from $R$ to $R$ such that $f(x)=x^2-1, g(x)=\sqrt{x^2+1}$ and $h(x)= \begin{cases}0, \text { if } & x \leq 0 \\ x, \text { if } & x \geq 0\end{cases}$ consider the following statements

(i) fog is invertible

(ii) $h$ is an identify function

(iii) $f \circ g$ is not invertible

(iv) $(h \circ f \circ g) x=x^2$

Then, which one of the following is true ?

AP EAPCET 2024 - 22th May Evening Shift
5
The domain of the real valued function $f(x)=\sqrt{9-\sqrt{x^2-144}}$ is
AP EAPCET 2024 - 22th May Morning Shift
6
The real valued function $f: R \rightarrow\left[\frac{5}{2}, \infty\right)$ defined by $f(x)=|2 x+1|+|x-2|$ is
AP EAPCET 2024 - 21th May Evening Shift
7
If $3 f(x)-2 f(1 / x)=x$, then $f(2)=$
AP EAPCET 2024 - 21th May Evening Shift
8
The domain of the real valued function $f(x)$ $=\log _2 \log _3 \log _5\left(x^2-5 x+11\right)$ is
AP EAPCET 2024 - 21th May Morning Shift
9
The range of the real valued function $f(x)=\left(\frac{x^2+2 x-15}{2 x^2+13 x+15}\right)$ is
AP EAPCET 2024 - 21th May Morning Shift
10
$f: R \rightarrow R$ is defined by $f(x+y)=f(x)+12 y, \forall x, y \in R$. If $f(1)=6$, then $\sum_{r=1}^n f(r)=$
AP EAPCET 2024 - 20th May Evening Shift
11
The domain of the real valued function $f(x)=\sqrt{2+x}+\sqrt{3-x}$ is
AP EAPCET 2024 - 20th May Evening Shift
12
Let $f(x)=3+2 x$ and $g_n(x)=(f \circ f \circ f o \ldots$ in times $)(x)$, $\forall n \in N$ if all the lines $y=g_n(x)$ pass through a fixed point $(\alpha, \beta)$, then $\alpha+\beta=$
AP EAPCET 2024 - 20th May Morning Shift
13

    Let $a > 1$ and $0 < \mathrm{b} < 1$. If $f: R \rightarrow[0,1]$ is defined by $f(x)=\left\{\begin{array}{ll}a^x, & -\infty < x < 0 \\ b^x, & 0 \leq x < \infty\end{array}\right.$, then $f(x)$ is

AP EAPCET 2024 - 20th May Morning Shift
14
If $P(x)=x^5+a x^4+b x^3+c x^2+d x+e$ is a polynomial such that $P(0)=1, P(1)=2, P(2)=5, P(3)=10$ and $P(4)=17$, then $P(5)=$
AP EAPCET 2024 - 20th May Morning Shift
15
If a real valued function $f:[a, \infty) \rightarrow[b, \infty)$ defined by $f(x)=2 x^2-3 x+5$ is a bijection. Then, $3 a+2 b=$
AP EAPCET 2024 - 19th May Evening Shift
16
The domain of the real valued function $f(x)=\frac{1}{\sqrt{\log _{0.5}(2 x-3)}}+\sqrt{4-9 x^2}$ is
AP EAPCET 2024 - 19th May Evening Shift
17
If a function $ f:R \rightarrow R $ is defined by $ f(x) = x^3 - x $, then $ f $ is
AP EAPCET 2024 - 18th May Morning Shift
18
If $ f(x) = \sqrt{x - 1} $ and $ g(f(x)) = x + 2x^2 + 1 $, then $ g(x) $ is
AP EAPCET 2024 - 18th May Morning Shift
19
For real values of $ x $ and $ a $, if the expression $ \frac{x^3 - 3x^2 - 3x + 1}{2x^2 - 3x + 1} $ assumes all real values, then
AP EAPCET 2024 - 18th May Morning Shift
20
$f(x+h)=0$ represents the transformed equation of the equation $f(x)=x^4+2 x^3-19 x^2-8 x+60=0$. If this transformation removes the term containing $x^3$ from $f(x)=0$, then $h=$
AP EAPCET 2024 - 18th May Morning Shift
21

$$f(x)=\log \left(\left(\frac{2 x^2-3}{x}\right)+\sqrt{\frac{4 x^4-11 x^2+9}{|x|}}\right) \text { is }$$

AP EAPCET 2022 - 5th July Morning Shift
22

Let $$f: R-\left\{\frac{-1}{2}\right\} \rightarrow R$$ be defined by $$f(x)=\frac{x-2}{2 x+1}$$. If $$\alpha$$ and $$\beta$$ satisfy the equation $$f(f(x))=-x$$, then $$4\left(\alpha^2+\beta^2\right)=$$

AP EAPCET 2022 - 5th July Morning Shift
23

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

AP EAPCET 2022 - 4th July Evening Shift
24

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

AP EAPCET 2022 - 4th July Morning Shift
25

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

AP EAPCET 2022 - 4th July Morning Shift
26

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

AP EAPCET 2021 - 20th August Morning Shift
27

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

AP EAPCET 2021 - 20th August Morning Shift
28

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

AP EAPCET 2021 - 20th August Morning Shift
29

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

AP EAPCET 2021 - 19th August Evening Shift
30

The domain of the function $$f(x)=\frac{1}{[x]-1}$$, where $$[x]$$ is greatest integer function of $$x$$ is

AP EAPCET 2021 - 19th August Evening Shift
31

Let $$f: R \rightarrow R$$ be a function defined by $$f(x)=\frac{4^x}{4^x+2}$$, what is the value of $$f\left(\frac{1}{4}\right)+2 f\left(\frac{1}{2}\right)+f\left(\frac{3}{4}\right)$$ is equal to

AP EAPCET 2021 - 19th August Evening Shift
32

Let $$f: R \rightarrow R$$ and $$g: R \rightarrow R$$ be defined by $$f(x)=2 x+1$$ and $$g(x)=x^2-2$$ determine $$(g \circ f)(x)$$ is equal to

AP EAPCET 2021 - 19th August Morning Shift
33

Given, the function $$f(x)=\frac{a^x+a^{-x}}{2},(a>2)$$, then $$f(x+y)+f(x-y)$$ is equal to

AP EAPCET 2021 - 19th August Morning Shift
34

If $$f$$ is a function defined on $$(0,1)$$ by $$f(x)=\min \{x-[x],-x-[x]\}$$, then $$(f \circ f o f o f)(x)$$ is equal to $$\rightarrow([\cdot]$$ greatest integer function)

AP EAPCET 2021 - 19th August Morning Shift
35

If $${({x^2} + 5x + 5)^{x + 5}} = 1$$, then the number of integers satisfying this equation is

AP EAPCET 2021 - 19th August Morning Shift
36

If $$\frac{x^4}{(x-1)(x-2)}=f(x)+\frac{A}{x-1}+\frac{B}{x-2}$$, then

AP EAPCET 2021 - 19th August Morning Shift
37

Which statement among the following is true?

(i) the function $$f(x)=x|x|$$ is strictly increasing on $$R-\{0\}$$.

(ii) the function $$f(x)=\log _{(1 / 4)} x$$ is strictly increasing on $$(0, \infty)$$.

(iii) a one-one function is always an increasing function.

(iv) $$f(x)=x^{1 / 3}$$ is strictly decreasing on $$R$$

AP EAPCET 2021 - 19th August Morning Shift
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