Inverse of a Function

Q. Which of the following are linear functions?

1. -x + 2
2. x + $\frac{1}{2}$
3. $x^2$ + 9x
4. $\frac{1}{x}$
5. $\frac{-2}{5}$x
6. 4x - 1
7. 5|x| -1
8. x

Q. $lo{g}_{7}lo{g}_7\sqrt{7\left(\sqrt{7\sqrt{7}}\right)}=$

1. $3lo{g}_{2}7$
2. $Noneofthese$
3. $1-3lo{g}_{3}7$
4. $1-3lo{g}_{7}2$

Q. Prove that root of equation $a{x}^2+bx+c=0$ is$\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Q. Inverse exists for a function which is

1. Injective
2. Surjective
3. Bijective
4. Many-one

Q. If $2x^2+px+6=\left(2x-a\right)\left(x-2\right)$ Find the value of $a,p.$

1. $a=3$ and $p=-7$
2. $a=-3$ and $p=7$
3. $a=-3$ and $p=-7$
4. $a=3$ and $p=7$

Q.

Find the quotient.

$-32÷(-4)$

Q. Find the product of $\cos {30}^0.\cos {45}^0.\cos {60}^0$

1. none of these
2. $\frac{\sqrt{3}}{4\sqrt{2}}$
   
3. $\frac{\sqrt{3}}{2\sqrt{2}}$
4. $\frac{\sqrt{3}}{\sqrt{2}}$
   

Q. Domain of the function $f\left(x\right)=\sqrt{\frac{5-|x|}{|x|-6}}$ is

फलन $f\left(x\right)=\sqrt{\frac{5-|x|}{|x|-6}}$ का प्रांत है

1. [–5, 5]
2. (–∞, –6) ∪ [–5, 5] ∪ [6, ∞)
   
3. (–6, –5] ∪ [5, 6)
   
4. R
   

Q. If f(x) = |x| + 1, g(x) = 2x - 1, and fog(x) = 2, find the sum of values of x.

1. 1