Question

Find the domain and the range of the real function f defined by f (x)=|x-1|

Answer 1

Hope it will help you

Answer 2

function f is defined by f(x) = |x - 1|

f(x) is modulus function. so, first we have to break modulus .

case 1 :- when x ≥ 1

f(x) = x - 1

case 2 :- when x < 1

f(x) = 1 - x

if we draw the graph of given function. we will see graph as shown in figure.

now, domain of function belongs to all real numbers because there is no any point where function is undefined.

range of function belongs to all real numbers greater than or equal to 0. because for all value of x , f(x) will be positive.

hence, Domain $\in\mathbn{R}$
Range $\in\mathbb{R}^+\cup\{0\}$