Range

Q.

Range of the function $f\left(x\right)=\frac{x^2+x+2}{x^2+x+1};xϵR$ is

1. $(1,\infty )$

2. $(1,\frac{11}{7})$

3. $(1,\frac{7}{3}]$

4. $(1,\frac{7}{5})$

Q.

Let A = {1, 2, 3, 4} and B = {1, 4, 9, 16, 25} and R be a relation defined from A to B as

R = {(x, y): x $ϵ$ A, y $ϵ$ B and y =$x^2$}

(i) Depict this relation using arrow diagram.

(ii) Find domain of R.

(iii) Find range of R.

(iv) Write codomain of R.

(v) Does the truthfulness and honesty may have any relation?

Q.

The domain and range of the signum function is:

1. R, [0, ∞]

2. R - {0}, {-1, 1}

3. R, R

4. (- ∞, ∞), {-1, 0, 1}

Q. Let $f\left(x\right)=sin\left[\frac{\pi }{6}sin\left(\frac{\pi }{2}sinx\right)\right]\forall xϵR\text{and}g\left(x\right)=\frac{\pi }{2}sinx\forall xϵR$. Let (fog) (x) denotes f{g(x)} and (gof) (a) denotes g{f(x)}. Then, which of the following is / are true?

1. Range of f is $[-\frac{1}{2},\frac{1}{2}]$
2. Range of fog is $[-\frac{1}{2},\frac{1}{2}]$
3. $li{m}_{x\to 0}\frac{f\left(x\right)}{g\left(x\right)}=\frac{\pi }{6}$
4. There is an x $ϵ$R such that (gof) (x) = 1

Q.

Let $f=\left[\right(x,\frac{x^2}{1+x^2}):xϵR]$ be a function from R into R. Determine the range of f.

Q.

The range of $f\left(x\right)=\frac{2x}{2+3x}$ is

1. $R$

2. $R-\left\{\frac{2}{3}\right\}$

3. $R-\left\{\frac{-2}{3}\right\}$

4. $R^{+}$

Q. The range of the function f(x)=\operatorname{cos^2x-5\operatorname{cosx-9 is

Q.

Let $X=\{2,3,4,5\}$ and $Y=\{7,9,11,13,15,17\}$. Define a relation f from X to Y by:
$f=\left\{\right(x,y):xϵX,yϵY\text{and}y=2x+3\}$

(i) Write f in roster form.

(ii) Find dom(f) and range (f).

(iii) Show that f is a function from X to Y.

Q.

What is the range of the following data?
23, 45, 34, 21, 89, 45, 47, 91

1. 69

2. 71

3. 70

4. 56

Q. The entire graphs of the equation $y=x^2+kx-x+9$ is strictly above the x-axis if and only if

1. k<7
2. -5<k<7
3. k>-5
4. -7<k<5

Q.

What is the range of the following data: 6, 10, 7, 12, 10, 13, 13, 4, 8, 12

1. 10

2. 9

3. 11

4. 13

Q. Range of the function $f\left(x\right)=\frac{x^2+x+2}{x^2+x+1};xϵR$ is

1. $(1,\frac{7}{3}]$
2. $(1,\frac{7}{5})$
3. $(1,\infty )$
4. $(1,\frac{11}{7})$

Q. 44. f(x) = (2008^x + 2008^(-x))/2. Find its range.

Q.

A: The minimum value of 'y' for the expression y = 2 $x^2$ + 4x + 5 occur at x =______

B: The maximum value of expression -3 $x^2$ + 12x + 5 is _______

1. 2, 27

2. 2, 17

3. -1, 27

4. -1, 17

Q. Let $a_1,a_2,a_3,\dots ,a_n$ be the integers which are not included in the range of $f\left(x\right)=\frac{40}{(x-5)(x+1)},$ where $a_i>a_{i+1}$ for each $i=1,2,3,\dots ,n$. If $\sum _{i=1}^n$ ${}^{5-a_i}{C}_{i-1}={}^x{C}_y$, then $x+y$ can be

1. $14$
2. $21$
3. $16$
4. $15$

Q.

Let A = {1, 2, 3, …, 30} and R be the relation “is one-fifth of” on A. Then the range of R is

1. {5, 10, 15, 20, 25, 30}

2. {1, 2, 3, 4, 5}

3. {1, 2, 3, 4, 5, 6}

4. {1, 2, 3, 4, 5, 6, 10, 15, 20, 25, 30}

Q.

Find the range for the function f(X) = - |x|, where x is a real number.

1. all positive real numbers

2. all real numbers less than or equal to zero.

3. all natural numbers

4. all integers

Q.

Identify the domain and range of the function f(x), defined in N, as below:

1. {1, 2, 3} and {2, 4, 6}

2. {1, 3, 5} and {2, 4, 6}

3. {1, 2, 3, 4, 5} and {2, 3, 5}

4. {1, 2, 4} and {2, 4, 6}

Q. find the mean of first five even number

Q. Let be a function from R into R . Determine the range of f .

Q. The range of the function $f\left(x\right)=\frac{[x-3]}{\left[x\right]-3}$ in its domain is
($[.]$ represents the greatest integer function)

1. $[-1,1]$
2. $R$
3. $\left\{1\right\}$
4. $R-\left\{1\right\}$

Q.

The set of values of a for which $4^t-(a-4)2^t+\frac{9a}{4}$ < 0 $\forall tϵ(1,2)$ is

1. 

2. 

3. ( , -48 )

4. 

Q.

To receive grade A in a course one must obtain an average of 90 marks or more in five papers, each of 100 marks. If Tanvy scored 89, 93, 95 and 91 marks in first four papers, find the minimum marks that she must score in the last paper to get grade A in the course.

Q.

If $\alpha ,\beta ,\gamma$ are the roots of $x^3-x^2-1$ = 0, then the value of $\frac{1+\alpha }{1-\alpha }+\frac{1+\beta }{1-\beta }+\frac{1+\gamma }{1-\gamma }$ is equal to:

1. -5

2. -6

3. -2

4. -7

Q. find range of the function y = 3x^2 - 6x + 11 , if x e [-1, 5)

Q. if w, x, y, z∈ R+ and 256xyzw≥slant{(w+x+y+z)}^4and 3w+5x+7y+9z=24, then roots of equation (w+x)t^2+yzt+\sqrt{x+y+w+z}=0 are

Q.

The variance of following data 5, 6, 4, 2, 3, 8, 9 is:

1. 2.36

2. 5

3. 4.58

4. 3.5

Q. The range of the function f(x) =x^6+x^4+2x^2+1+2/x^2+1/x^4+1/x^6

Q. 9. what is the range of 3cosx-sinx and 3sinx-cosx

Q. If $A=\{x:|x|\le 5;x\in Z-\{0\left\}\right\}$, $B=\{x:x\le 100;x\in W\}$ and $f:A\to B$ is a function defined by $f\left(x\right)=x^2+1$, then the number of elements in the range of $f$ that lie in $[5,26)$ is

1. $5$
2. $3$
3. $4$
4. $2$