Definition of Function

Q.

Find the values of x in each of the following:

$\left(i\right)\frac{log144}{log12}=logx$

$\left(ii\right)\frac{log125}{log25}=x$

$\left(iii\right)lo{g}_{x}4+lo{g}_{x}16+lo{g}_{x}64=12$

Q. If the graph shown below represents $f\left(x\right)=\sin x$, then which of the following options describe $p\left(x\right)=\sin 2x$?

1. 
2. 
3. 
4. 

Q. The correct option(s) for the function $f\left(x\right)=\sqrt{\left(\right[x]-1)}+\sqrt{(4-[x\left]\right)}$ is/are
(where [.] represents the greatest integer function)

Q. Which of the following is/are functions?

1. 
2. 
3. 
4. 

Q.

Find the domain and range of the function $f\left(x\right)=\frac{|x-4|}{x-4}$.

Q. 39. What is the domain and range of F(x)=|x-3| .Also draw its graph

Q. Which of the following is/are functions?

1. 
2. 
3. 
4. 

Q. 24. If A and B are independent events associated to some experiment E such that P(A intersection B) = 2/15 and P(A intersection B) = 1/6, then P(B) in equal to

Q. Which among the following relations defined on $R$ is/are functions

1. $\left(i\right)$
2. $\left(ii\right)$
3. $\left(iv\right)$
4. $\left(v\right)$

Q. Which of the following is not a function?

1. 
2. 
3. 
4. 

Q. Which among the following is\are function(s)

1. 
2. 
3. 
4. 

Q. If $f\left(x\right)=x^5-5x^4+5x^3-10$ has local maximum and minimum at $x=a$ and $x=b$ respectively, then $(a,b)$ is

1. $(0,1)$
2. $(3,0)$
3. $(1,3)$
4. $(3,1)$

Q. If $A=\{1,2,3,4\},$ then which among the following relations are not functions from $A$ to itself

1. $f_1=\left\{\right(x,y)|y=x+1,\forall x,y\in A\}$
2. $f_2=\left\{\right(x,y)|x+y>4,\forall x,y\in A\}$
3. $f_3=\left\{\right(x,y)|y<x,\forall x,y\in A\}$
4. $f_4=\left\{\right(x,y)|x+y=5,\forall x,y\in A\}$
   

Q.

$f\left(x\right)=\mp \sqrt{1-x^2}$ is a function

1. False

2. True

Q. Which among the following relations between $x,y$ doesn't represent a function

1. $(x-1{)}^2+(y-3{)}^2=5^2,x\in [-4,6],y\in R$
2. $y^2=4x,x\in [0,\infty ),y\in R$
3. $x^2=4y,x,y\in R$
4. $y=2x+5^2,x,y\in R$