Composition of Function

Q.

What is a magneson reagent and explain its uses?

Q.

When $x^{200}+1$ is divided by $x^2+1$, the remainder is equal to

1. 1

2. 

3. 2x-1

4. 2

Q. $\text{Find}fog\text{when}f\left(x\right)=2x+1$ and
$g\left(x\right)=x^2-2$.

1. $2x^2+3$
2. $2x^2-3$
3. $-2x^2-3$
4. $-2x^2+3$

Q. $\text{If}f\left(x\right)=x^2+1,\text{then find}fof$.

1. $x^2+1$
2. $x^4+2x^2+1$
3. $x^4+2x^2+2$
4. $x^2+2x^2+2$

Q.

$f\left(x\right)=a{x}^7+b{x}^3+cx-5$ where a, b, c are constants. If $f(-7)=7$ then $f\left(7\right)$ equals to

1. -17

2. -7

3. 14

4. 21

Q.

If $a+b=\sqrt{5}$ and $a-b=\sqrt{3}$, then the value of $a^2+b^2$ is equal to 4.

1. True

2. False

Q. Find x if , gff(x) = fgg(x), given f (x) = 3x +1 and g(x) = x + 3

1. x=-2
2. x=1
3. x=2
4. x=-1

Q. If f (x) = 3x − 2 , g(x) = 2x + k and f o g = g o f , then find the value of k.

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

Q.

If $f\left(x\right)$ and $g\left(x\right)$ are twice differentiable functions on $(0,3)$ satisfying $f\left(x\right)=g\left(x\right),f\left(1\right)=4,g\left(1\right)=6,f\left(2\right)=3,g\left(2\right)=9$, then $f\left(1\right)-g\left(1\right)$ is equal to:

1. $4$

2. $-4$

3. $0$

4. $-2$

Q. $\text{If}f\left(x\right)=x^2-1,\text{then find}fofof.$

1. $x^8+4x^4-4x^6-1$
2. $x^4-2x^2$
3. $x^8+4x^4-4x^6$
4. $x^2-1$

Q. If f (x) = 2x + 3 , g(x) = 1−2x and h(x) = 3x, then find f o (g o h).

1. 5 − 4x
2. 5 + 4x
3. 5 − 12x
4. 5 + 12x

Q.

Let f(x) = $x^2$ and g(x) = 3x + 4 . Find the value of $\frac{(f+g)\left(x\right)}{(f-g)\left(x\right)}$ when x = 1

1. 4/3

2. 3/4

3. -4/3

4. -3/4

Q. If f(x) = 2x - 5, g(x) = x + 2, and fog(x) = 5, find the value of x.

1. 3

Q.

The value of $2^n\{1\times 3\times \mathrm{5.....}(2n-3)\times (2n-1\left)\right\}$ is $\frac{\left(2n\right)!}{n!}$

1. 

2. 

Q.

A solution is said to have ___ character when its pH value is greater than seven. (basic/acidic)

Q.

If $x+x^{-1}=11$, evaluate $x^2+x^{-2}$.

1. 119
2. 120
3. 121
4. 122

Q. If $a^2-2a+1=0$, then the value of $a$

Q. $\text{If}f\left(x\right)=x^2-1,\text{and}g\left(x\right)=x-2,$ $\text{then find a, if}gof\left(a\right)=1.$

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

Q. $\text{If}f\left(x\right)=2x-1,g\left(x\right)=\frac{x+1}{2},\text{then}fog=$___.

1. $x$
2. $2x$
3. 1
4. 0

Q. $\mathrm{Find}y\mathrm{if}\mathrm{fof}\left(y\right)=5\mathrm{and}f\left(y\right)=3y-1$

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

Q.

What are Normal salts? Give three examples.

Q.

Find the value of $2p^{2}q-3p{q}^2+2p-3q+1$, when $p=3$ and $q=-3$.

Q. $\text{If}f\left(x\right)=x^2-1,\text{and}g\left(x\right)=x-2,$ $\text{then find a, if}gof\left(a\right)=6.$

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

Q.

If $f\left(x\right)=x^2+2bx+2c^2$ and $g\left(x\right)=-x^2-2cx+b^2$ such that in $f\left(x\right)>maxg\left(x\right)$, then the relation between $b$ and $c$, is

1. $|c|>|b|\sqrt{2}$

2. $0<c<b\sqrt{2}$

3. No real value of b &c

4. $|c|<|b|\sqrt{2}$

Q. $\text{If}f\left(x\right)=x^2-1,\text{and}g\left(x\right)=x-2,$ $\text{then find a, if}gof\left(a\right)=6.$ [2 marks]

Q. $\text{The function}fog\left(x\right)\text{can be defined if}$ ___

1. Domain of $g\left(x\right)$ $\subseteq$ Domain of $f\left(x\right)$
2. Range of $g\left(x\right)$ $\subseteq$ Domain of $f\left(x\right)$
3. Domain of $g\left(x\right)$ $\subseteq$ Range of $f\left(x\right)$
4. Range of $g\left(x\right)$ $\subseteq$ Range of $f\left(x\right)$

Q. $\text{If}f\left(x\right)=2x^2\text{and}g\left(x\right)=\frac{1}{3x},\text{then}fog\text{is}$___

1. $\frac{3}{2x^2}$
2. $\frac{2}{3x^2}$
3. $\frac{2}{9x^2}$
4. $\frac{1}{6x^2}$

Q.

Describe the process of neutralization with the help of an example.

Q.

If $\sqrt{\frac{125a^6{b}^4{c}^2}{5a^4{b}^2}}=x$ then what is the value of $\frac{x^2}{abc}$?

1. $125a^2{b}^2{c}^2$

2. $25abc$

3. $5abc$

4. $25a^2{b}^2{c}^2$

Q.

If x ∝ y, then $x^3\propto y^4$

1. True

2. False