Functions Test 52

Result

Functions Test 52

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Show that the function $$f:[0, \infty)\rightarrow [0, \infty)$$ defined by $$f(x)=\dfrac{2x}{1+2x}$$ is?

A
One-one and onto

B
One-one but not onto

C
Not one-one but onto

D
Neither one-one nor onto

Solution
Question 2
1 / -0

The domain of the function $$\text{f(x)}={ \text{log} }_{ 5 }({\text{ log} }_{ 4 }\{ { \text{log} }_{ 4/\pi }({ \tan }^{ -1 }x)^{ -1 }\} )$$ is

A
$$\mathbb{R}$$

B
$$\left[0, 1\right]$$

C
$$\left(0, 1\right]$$

D
$$\left(0, 1\right)$$

Solution
Question 3
1 / -0

The domain of $$f(x)=\dfrac{1}{\sqrt{(x-1)(x-2)(x-3)}}$$ is

A
$$(1, 2)$$

B
$$(3, \infty)$$

C
$$(2, 3)$$

D
$$(-\infty, 1)$$

Solution
Question 4
1 / -0

The domain of $$f(x)=\log_{x}\log_{2}\left(\dfrac {1}{x-1/2}\right)$$ is

A
$$\left(\dfrac {1}{2},1\right) \cup \left(1,\dfrac {3}{2}\right)$$

B
$$\left(\dfrac {1}{2},\dfrac {3}{2}\right)$$

C
$$\left[\dfrac {1}{2},\dfrac {3}{2}\right]$$

D
$$\left(\dfrac {1}{2},\dfrac {3}{2}\right]$$

Solution
Question 5
1 / -0

Let $$f:R\rightarrow R$$ be defined by $$f(x)=\dfrac {x|x|}{2}+\cos x+1$$ then $$f(x)$$ is

A
One-one only

B
Onto only

C
Neither one-one nor onto

D
Bijection

Solution
Question 6
1 / -0

If $$P(S)$$ denotes the set of all subsets of a given set S, then the number of one-to-one functions from the set $$S=\{1,2,3\}$$ to he set $$P(S)$$

A
$$24$$

B
$$8$$

C
$$336$$

D
$$320$$

Solution
Question 7
1 / -0

$$\begin{aligned} \text { If } A & = \{ x | x / 2 \in Z , 0 \leq x \leq 10 \} \\ B & = \{ x | x \text { is one digit prime } \} \\ C & = \{ x | x / 3 \in N , x \leq 12 \} \end{aligned}$$,
Then $$A \cap ( B \cup C )$$ is equal to-

A
$$\{ 2,6 \}$$

B
$$\{3,6,12 \}$$

C
$$\{ 2,6,12 \}$$

D
$$\{ 6,8 \}$$

Solution
Question 8
1 / -0

The function $$f:N\rightarrow N $$ defined by $$f\left( x \right) =x-5\left[ \dfrac { x }{ 5 } \right]$$, where $$N$$ is the set of natural numbers and $$[x]$$ denotes the greatest integer less then or equal to $$x$$ is

A
One-one and onto

B
One-one but not onto

C
Onto but not one-one

D
Neigher one-one nor onto

Solution

undefined
Question 9
1 / -0

Let $$f:R\rightarrow R$$ is defined as $$f(x)=\begin{cases} 2x+{ \alpha }^{ 2 },\ x \ge 2 \\ \frac { \alpha x }{ 2 } +10,\ x <2 \end{cases}$$. If $$f(x)$$ is onto function then set of values of $$\alpha$$ is

A
$$[1,4]$$

B
$$[-2,3]$$

C
$$(0,3]$$

D
$$[2,5]$$

Solution
Question 10
1 / -0

Let $$f(x)=\sqrt{\cos^{-1}\sqrt{1-x^{2}}-\sin^{-1}{x}}$$ then which of the following statement(s) is/are correct

A
Domain of $$f(x)$$ is $$[-1,1]$$

B
Domain of $$f(x)$$ is $$[0,1]$$

C
Range of $$f(x)$$ is $$\left\{0\right\}$$

D
Range of $$f(x)$$ is $$[0, \pi]$$

Solution