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# Domain of function, Co-domain, Range of function - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

## Quick Facts

• 32 Questions around this concept.

## Solve by difficulty

The domain of definition of the function $\dpi{100} f\left ( x \right )= \frac{3}{4-x^{2}}+\log_{10}\left ( x^{3} -x\right ),$ is

Let $\mathrm{f}: \mathbf{R}-\left\{\frac{-1}{2}\right\} \rightarrow \mathbf{R}$ and $\mathrm{g}: \mathbf{R}-\left\{\frac{-5}{2}\right\} \rightarrow \mathbf{R}$ be defined as $\mathrm{f}(\mathrm{x})=\frac{2 \mathrm{x}+3}{2 \mathrm{x}+1}$ and $\mathrm{g}(\mathrm{x})=\frac{|\mathrm{x}|+1}{2 \mathrm{x}+5}$. Then, the domain of the function fog is :-

If $f(x)=\left\{\begin{array}{cc}2+2 x, & -1 \leq x<0 \\ 1-\frac{x}{3}, & 0 \leq x \leq 3\end{array} ; g(x)=\left\{\begin{array}{cc}-x, & -3 \leq x \leq 0 \\ x, & 0<x \leq 1\end{array}\right.\right.$, then range of $(f \circ g)(x)$ is

## Concepts Covered - 1

Domain of function, Co-domain, Range of function

Domain

All possible values of x for f(x) is defined (f(x) is a real number) is known as domain.

If a function is defined from A to B i.e. f: A⇾B, then all the elements of set A is called Domain of the function.

Co-domain

If a function is defined from A to B i.e. f: A⇾B, then set B is called Co-domain of the function.

Range

The set of all possible values of f(x) for every x belonging to the domain is known as Range of this function.

For example, let A = {1, 2, 3, 4, 5} and B = {1, 4, 8, 16, 27, 64, 125}. The function f : A -> B is defined by f(x) = x3. So here,

Domain : Set A

Co-Domain : Set B

Range : {1, 8, 27, 64, 125}

The range is always a subset of co-domain and Range can be equal to co-domain in some cases.

Note: If only the formula is given, then co-domain is R, and domain and range have to be found.

• Domain in this case will be all the real values of x for which y is real
• Range is all the real values of y corresponding to values of x in the domain

Rules to find Domain

• If domain of f(x) is A and domain of g(x) is B, then domain of f(x)+g(x), f(x) - g(x), f(x) . g(x) is A ∩ B.
• For domain of f(x)/g(x), remove values of x for which g(x)=0, from A ∩ B.
• Domain of expressions of type $\sqrt{f(x)}$, we take the common values between A and values of x for which f(x) ≥ 0.
• Domain of polynomial function is R.
• Graphical method: we can also find domain if only the graph of function is given. We will learn this through the help of solved examples.

Methods to find Range

• Simple manipulations
• For range of y = f(x), we can first express x as a function of y: x = g(y). Now the domain of x = g(y) is same as the range of y = f(x)
• Graphical method: we can also find the range if only the graph of function is given.

We will learn these through the help of solved examples later

## Study it with Videos

Domain of function, Co-domain, Range of function

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