Question

Find the domain of the real valued function: f(x) = |x - 3|

Answer 1

The $\textbf{domain}$ of function $\textbf{f(x)}$ is the set of all values for which function is defined.

we have to find domain of function : f(x) = |x - 3|

here, function , f(x) is a modulus function.

so, we have to break it ,

case 1 :- when x ≥ 3

f(x) = x - 3

function is defined for all real value of x greater than equal to 3

case 2 :- when x < 3

f(x) = -(x - 3)

function is defined for all real value of x less than 3

so, domain of function $\in(-\infty,3]\cup(3,\infty)$

$\implies$ domain of function $\in\mathbb{R}$

Answer 2

Answer:

The \textbf{domain}domain of function \textbf{f(x)}f(x) is the set of all values for which function is defined.

we have to find domain of function : f(x) = |x - 3|

here, function , f(x) is a modulus function.

so, we have to break it ,

case 1 :- when x ≥ 3

f(x) = x - 3

function is defined for all real value of x greater than equal to 3

case 2 :- when x < 3

f(x) = -(x - 3)

function is defined for all real value of x less than 3

so, domain of function \in(-\infty,3]\cup(3,\infty)∈(−∞,3]∪(3,∞)

\implies⟹ domain of function \in\mathbb{R}∈R