Find the domain and range of the following function f(x)= 5|x-2| + 4

Domain-- All the real numbers.

Range--  [4,∞)

We are given a function f(x) as:

We know that domain of a function is the set of all the x-values where the function is well defined.

Also, we know that the modulus function is defined for all the real numbers and hence adding a constant does not change the domain of the function.

Hence, Domain of function is all the real numbers.

Also, we know that:

Hence, the Range is the set of all the real values greater than or equal to 4.

Hence,

Range= [4,∞)