Definition of Functions

Q. The solution set for x(x+2)^2(x-1)^5(2x-3)(x-3)^4>or equal to 0 is given by x belongs to [a, b] union [c, infinity) then the value of a+B+C=______

Q.

Q. If the function $f:R\to$ A given by $f\left(x\right)=\frac{x^2}{x^2+1}$ is a surjection, then A is

1. R
2. [0, 1]
3. (0, 1]
4. [0, 1)

Q. ${\left(\frac{x^a}{x^{-b}}\right)}^{a^2-ab+b^2}\times {\left(\frac{x^b}{x^{-c}}\right)}^{b^2-bc+c^2}\times {\left(\frac{x^c}{x^{-a}}\right)}^{c^2-ac+a^2}$

Q. Check if $(0,2)$ solution of the equation $x-2y=4$ or not:

Q. Prove that x=2x

Q.

Let f(x) be a function defined on [0, 1] such that $f\left(x\right)=\{\begin{array}{ccc}x,& ifxϵQ& \\ 1-x,& ifx\text{/}ϵQ& \end{array}$
Then, for all $xϵ[0,1],f\left(f\right(x\left)\right)=$

1. $x$

2. none of these

3. $1+x$

4. constant

Q.

If $g\left\{f\right(x\left)\right\}=|sinx|$ and $f\left\{g\right(x\left)\right\}=(sin\sqrt{x}{)}^2$, then

1. $f\left(x\right)=si{n}^{2}x,g\left(x\right)=\sqrt{x}$

2. $f\left(x\right)=x^2,g\left(x\right)=sin\sqrt{x}$

3. $f\left(x\right)=sinx,g\left(x\right)=|x|$

4. f and g cannot be determined

Q. The function given below will be a cubic function only if

1. c = 0
2. a = 0
3. d = 0
4. b = 0

Q. A real valued function $f\left(x\right)$ satisfies the function equation $f(x-y)=f\left(x\right)f\left(y\right)-f(a-x)f(a+y)$ where a is a given constant $f\left(0\right)=1,f(2a-x)$ is equal to

1. f(a) + f(a - x)
2. f(-x)
3. -f(x)
4. f(x)

Q. which of the following is true? 1) {2} belongs to {1, 2, 3} 2) ɸ belongs to {1, 2, 3} 3) {1, 2} belongs to {1, {2, 3}} 3) 0 belongs to {0, 1, 2

Q. $a^3+b^3=(a+b)(a^2-ab+b^2)$

1. False
2. True

Q.

$a^3-b^3=(a-b)(a^2-ab+b^2)$

1. True
2. False

Q. $a^3+b^3=(a+b)(a^2-ab+b^2)$

1. True
2. False

Q. Given a function $f$ such that $f\left(4\right)=5$ , then which of the following is/are true for $f$?

1. $f\left(x\right)\ne x+1$
2. $f\left(x\right)\ne 3x-2$
3. $f\left(x\right)\ne 4x-11$
4. $f\left(x\right)\ne 2x-3$

Q.

What is the solution to the system x + y = 5 and 3x - y = 3?

1. (-2, -3)

2. (2, -3)

3. (-2, 3)

4. (2, 3)

Q. state true or false: A x+By+C=0, represents a closed curve