CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

$$K(x)$$ is a function such that $$K(f(x))=a+b+c+d$$,
Where,
$$a=\begin{cases}0 & \text{ if f(x) is even}  \\ -1 & \text{ if f(x) is odd} \\ 2 & \text{ if f(x) is neither even nor odd} \end{cases}$$

$$b=\begin{cases}3 & \text{ if  f(x) is periodic} \\ 4 & \text{  if  f(x) is  aperiodic} \end{cases}$$

$$c=\begin{cases}5 & \text{ if  f(x) is  one one} \\ 6 & \text{  if  f(x) is many one} \end{cases}$$

$$d=\begin{cases}7 & \text{ if  f(x) is onto} \\ 8 & \text{  if  f(x) is into} \end{cases}$$
 
$$h:R\rightarrow R,h(x)=\left ( \displaystyle \frac{e^{2x}+e^{x}+1}{e^{2x}-e^{x}+1} \right )$$ 

On the basis of above information, answer the following questions.$$g(x) = sin(x)$$
$$K(g(x))=$$


A
15
loader
B
16
loader
C
17
loader
D
18
loader

Solution

The correct option is B $$16$$
$$g(x)=\sin(x)$$
Hence $$g(-x)=-g(x)$$, therefore an odd function.
It is periodic, with a period of $$\pi$$
$$sin(x)$$ is an onto function only for a co-domain of $$\left[\dfrac{-\pi}{2},\dfrac{\pi}{2}\right]$$ since its range is $$[-1,1]$$
Thus for $$R \rightarrow R$$ or a co-domain, R, it is an into function.
Also $$\sin(x)$$ is a many on one function since
$$\sin(x_{1})=\sin(x_{2})$$
Implies
$$x_{1}=(2n+1)\pi-x_{2}$$ where $$n\in W$$.
Hence
$$k(g(x))=-1+3+6+8$$
$$=16$$

Maths

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image