Function

Q. A relation ‘f’ is defined by f (x) = x${}^2$ - 2, where x $\in$ {−2, −1, 0, 3}. Is f a function?

1. Yes
2. No

Q. If X = {–5, 1, 3, 4} and Y = {a, b, c}, then which of the following relations are functions from X to Y ?

1. R${}_1$= {(–5, a), (1, a), (3, b)}
2. R${}_2$= {(–5, b), (1, b), (3, a), (4, c)}
3. R${}_3$ = {(–5, a), (1, a), (3, b), (4, c), (1, b)}
4. R${}_4$ = {(-5, c), (-5, b), (1, a), (3, a), (4, b), (4, c)}

Q. Forensic scientists can determine the height (in cms) of a person based on the length of their thigh bone. They usually do so using the function h(b) = 2.47b + 54.10, where b is the length of the thigh bone.
Find the length of the thigh bone if the height of a person is 147.96 cms

1. 48
2. 36
3. 46
4. 38

Q. If $f\left(x\right)=ax+b$, where $a$ and $b$ are integers, $f(–1)=–5$ and $f\left(3\right)=3$, then $a$ and $b$ are equal to , respectively.

1. $2$
2. $-2$
3. $3$
4. $-3$

Q. The distance 'S' (in kms) travelled by a particle in time ‘t’ hours is given by
$\text{S(t)}=\frac{{\text{t}}^2+2}{2}$.
Find the distance travelled by the particle after 8.5 hours approximately.

1. 37.13 kms
2. 38.26 kms
3. 38.06 kms
4. 38.36 kms

Q.

If a function $f\left(x\right)$ defined by $\left\{\begin{array}{l}a{e}^x+b{e}^{-x},-1\le x<1\\ c{x}^2,1\le x\le 3\\ a{x}^2+2cx,3<x\le 4\end{array}\right.$ be continuous for some $a,b,c\in Randf\left(0\right)+f\left(2\right)=e$, then the value of $a$ is:

1. $\frac{1}{(e^2-3e+13)}$

2. $\frac{e}{(e^2-3e-13)}$

3. $\frac{e}{(e^2+3e+13)}$

4. $\frac{e}{(e^2-3e+13)}$

Q. Let A = {1, 2} and B = {3, 6} and f and g be functions from A to B, defined by f(x) = 3x and g(x) = x² + 2. Show that f = g.
$\left[3\right]$

Q. $\text{A function}f:[-5,9]\to R$ is defined by :
$f\left(x\right)=\{\begin{array}{c}6x+1\text{if}-5\le x<2\\ 5x^2-1\text{if}2\le x<6\\ 3x-4\text{if}6\le x\le 9\end{array}$
Find the value of $f\left(6\right)$.

1. 14
2. 179
3. 37
4. 2

Q. If f(x) = x + 1, g(x) = 2x - 1, and h(x) = $x^2$, then fogoh(x) is a function.

1. quadratic
2. linear
3. cubic

Q.

If y = f : A $\to$ B, then which of the following is true if f(x) is a function in x.

(i) x must be able to take each and every value of A

(ii) one value of x must be related to one and only one value of y in set B.

1. Only (ii)

2. Both (i) and (ii)

3. None of these

4. Only (i)

Q. If f (x) = x${}^2$, find $\frac{\text{f(1.1) - f(1)}}{\text{1.1 - 1}}$

1. 2.1
2. 2.2
3. 2.3
4. 2.4

Q.

If $(x-1)$ divides $m{x}^3-2x^2+25x-26$ without remainder, find the value of $m$.

1. 2

2. 3

3. 4

4. 1

Q. If a function 'f' defined by f(x) = 2x + 3, then find the value of 'x' such that f(x) = f(1-x).

1. 2
2. $\frac{1}{2}$
3. 8
4. $-\frac{1}{2}$

Q. Which step in the following problem is wrong?
$a=b=1$
$a=b$
step-1: $a^2=ab$
step-2: $a^2-b^2=ab-b^2$
step-3: $(a+b)(a-b)=b(a-b)$
step-4: a + b = $\frac{b(a-b)}{a-b}$
$a+b=b$
$1+1=1$
$2=1$

1. Step-3
2. Step-4
3. Step-2
4. Step-1

Q. If $y=f\left(x\right)=\frac{ax-b}{bx-a},x\ne \frac{a}{b},|a|\ne |b|,$ then $f\left(y\right)=$

1. $x$
2. $-x$
3. $\frac{1}{x}$
4. $-\frac{1}{x}$

Q.

$\text{If}f\left(x\right)=\sqrt{1+x^2}\text{, then}$ ____

1. $f\left(xy\right)=f\left(x\right)+f\left(y\right)$
2. $f\left(xy\right)\le f\left(x\right)\times f\left(y\right)$
3. $f\left(xy\right)\ge f\left(x\right)\times f\left(y\right)$
4. $f\left(xy\right)=f\left(x\right)\times f\left(y\right)$

Q.

What do we mean by significant figure? (With examples of all cases possible)

Q. $\text{A function}f:[-5,9]\to R$ is defined by :
$f\left(x\right)=\{\begin{array}{c}6x+1\text{if}-5\le x<2\\ 5x^2-1\text{if}2\le x<6\\ 3x-4\text{if}6\le x\le 9\end{array}$

Find $\frac{f(-7)-f\left(6\right)}{f\left(4\right)+f(-2)}$.

1. $\frac{55}{98}$
2. $\frac{-55}{98}$
3. $\frac{55}{100}$
4. 4

Q. $\text{If the function}f:R\to R$ is defined by :
$f\left(x\right)=\{\begin{array}{c}\sqrt{x-1}\text{if}x\ge 1\\ 2\text{if}x<1\end{array}$
Find the value of $f\left(0\right)$.

1. 0
2. $\sqrt{-1}$
3. 2
4. -1

Q. State, giving reason, whether each of the following arrow diagram represent a function or not

Q. $\text{If the function}f:R\to R$ is defined by :
$f\left(x\right)=\{\begin{array}{c}x-2,\text{if}x<-1\\ 2,\text{if}-1\le x\le 1\\ x+3,\text{if}x>1\end{array}$
Find the value of $f\left(0\right)$.

1. 3
2. can't be found
3. -2
4. 2

Q. $\text{If the function}f:R\to R$ is defined by :
$f\left(x\right)=\{\begin{array}{c}2x+7,x<2\\ 3x-2,x\ge 2\end{array}$
Find the value of $f\left(2\right)$.

1. 4
2. 5
3. 9
4. 1

Q. $\text{A function}f:[-5,9]\to R$ is defined by :
$f\left(x\right)=\{\begin{array}{c}6x+1\text{if}-5\le x<2\\ 5x^2-1\text{if}2\le x<6\\ 3x-4\text{if}6\le x\le 9\end{array}$

Find $f\left(4\right)+f\left(8\right)$.

1. 99
2. 79
3. 24
4. 199

Q.

If $y=f\left(x\right),$ where $f:A\to B$ is a function in $x,$ then which of the following statements is true?

(i) Every element of $A$ needs to have an image.

(ii) $x\in A$ must be related to one and only one value of $y$ of $B.$

1. Statement (i) is true, but statement (ii) is false.

2. Statement (ii) is true, but statement (i) is false.

3. Both statements (i) and (ii) are true.

4. Neither statement (i) nor statement (ii) is true.

Q.

How many of the following are functions ?

(i) f(x) = $x^5;\{-1,0,1\}\to \{0,1,2\}$

(ii) f(x) = $\pm \sqrt{x};\{0,4,9\}\to \{0,2,-2,3,-3\}$

(iii) f(x) = $\sqrt{x};\{0,4,9\}\to \{0,2,-2,3,-3\}$

(iv) f(x) = $x^2;\{0,1,2\}\to \{0,1,2,3,4\}$

1. (ii)&(iii)

2. (i)

3. (iii)

4. (iii) & (iv)

Q.

How many of the following are functions ?

(i) f(x) = $x^5;\{-1,0,1\}\to \{0,1,2\}$

(ii) f(x) = $\pm \sqrt{x};\{0,4,9\}\to \{0,2,-2,3,-3\}$

(iii) f(x) = $\sqrt{x};\{0,4,9\}\to \{0,2,-2,3,-3\}$

(iv) f(x) = $x^2;\{0,1,2\}\to \{0,1,2,3,4\}$

1. (i)

2. (ii)&(iii)

3. (iii)

4. (iii) & (iv)

Q.

If the relation f is defined by $f\left(x\right)=\{\begin{array}{cc}{x}^2,& 0\le x\le 3\\ 3x,& 3\le x\le 10\end{array}$
and the relation g is defined by $g\left(x\right)=\{\begin{array}{cc}{x}^2,& 0\le x\le 2\\ 3x,& 2\le x\le 10\end{array}$
then,

1. 'f' is a function and 'g' is not a function

2. 'g' is a function and 'f' is not a function

3. Both 'f' and 'g' are functions

4. neither 'f' nor 'g' are functions

Q. $\text{If the function}f:R\to R$ is defined by :
$f\left(x\right)=\{\begin{array}{c}\sqrt{x-1}\text{if}x\ge 1\\ 2\text{if}x<1\end{array}$
Find the value of $f\left(1\right)$.

1. 2
2. 1
3. 0
4. 3

Q. Let f(x) = $\frac{2x+3}{x-2}$, where x$\ne$2 and x$\in$R. Find $\frac{1}{3}$f(4).

1. $\frac{11}{3}$
2. $\frac{11}{6}$
3. $\frac{1}{3}$
4. - $\frac{11}{3}$

Q.

Pick the graph(s) which corresponds to a function.

1. 

2. 

3. 

4.