What is the domain and range of this function

sqrt(x-2)

Domain is x ≧ 2
Range is f (x) ≧ 0.

Domain is the possible values of x for the function to be real. Hence it is

x ≥ 2 (got from x − 2 ≥ 0)

Range is the possible real values of the function. it is

−∞ ≤ f(x) ≤ ∞

Not that even though squares can't be negative, square root can be negative. Eg: √4 = ±2. Hence saying range is f(x) ≥ 0 is wrong.

1) For sqrt(x - 2) , x - 2 must a non negative real number. hence

the domain is the set of all values of x such that: x - 2 >= 0 , solve x >= 2 , domain (-infinity , 2]

2) The range is the value of sqrt(x - 2) for all x in the domain.

if x is such that x - 2 >=0 ,then sqrt(x - 2) >= 0. Hence the range is the set [0 , +infinity).

more at www.analyzemath.com

f(x) = √(x - 2)

To be defined, (x - 2) must be a positive value (or null).

x - 2 ≥ 0 → then you add 2 on each side

x - 2 + 2 ≥ 0 + 2 → then you simplify

x ≥ 2

Domain : D = [2 ; +∞[

Function is f(x): domain is the values of X and range is the results u get when u insert X values.

Domain is x >= 2, Range is y>=0.

Dom : x>=2

Ran: y>=0

Its easy newbs