Answer

Verified

435.3k+ views

**Hint:**In mathematics, a map is often used as a synonym for a function, but may also refer to some generalizations. Originally, this was an abbreviation of mapping, which often refers to the action of applying a function to the elements of its domain. A function is a special type of relation in which each element of the domain is paired with exactly one element in the range. A mapping shows how the elements are paired. It’s like a flow chart for a function, showing the input and output values. Maps present information about the world in a simple, visual way. They teach about the world by showing sizes and shapes of countries, locations of features, and distances between places. Maps can show distributions of things over Earth, such as settlement patterns.

**Complete step-by-step answer:**We have $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}, \mathrm{f}(\mathrm{x})=\cos \mathrm{x}$

Let $\mathrm{f}\left(\mathrm{x}_{1}\right)=\mathrm{f}\left(\mathrm{x}_{2}\right)$

$\Rightarrow \cos x_{1}=\cos x_{2}$

$\Rightarrow \mathrm{x}_{1}=2 \mathrm{n} \pi \pm \mathrm{x}_{2}, \mathrm{n} \in \mathrm{Z}$

For example, when we use the function notation $f: R \rightarrow R,$ we mean that $f$ is a function from the real numbers to the real numbers. In other words, the domain of $\mathrm{f}$ is the set of real number $\mathrm{R}$ (and its set of possible outputs or codomain is also the set of real numbers $\mathbf{R}$ ).

Above equation has infinite solutions for $\mathrm{x}_{1}$ and $\mathrm{x}_{2}$.

Thus $\mathrm{f}(\mathrm{x})$ is many one function

Also the range of $\cos \mathrm{x}$ is [-1,1], which is a subset that is given a co-domain $\mathrm{R}$.

Hence function is not onto.

**Hence, the correct answer is Option A.**

**Note:**An example of mapping is creating a map to get to your house. An example of mapping is identifying which cell on one spreadsheet contains the same information as the cell on another spreadsheet. (mathematics) A function that maps every element of a given set to a unique element of another set; a correspondence. "Map" is a more general term than "translate", "rotate", etc.; it just means "transform every item in the domain" (and "domain" means "group of things we are transforming"). So, the "mapping notation" we have mentioned, like $(\mathrm{x}, \mathrm{y}) \rightarrow(\mathrm{x}+1, \mathrm{y}+1),$ is a way we can express any kind of transformation in the geometric plane.

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

How do you graph the function fx 4x class 9 maths CBSE

Which are the Top 10 Largest Countries of the World?

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

The largest tea producing country in the world is A class 10 social science CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE