Question

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

Answer 1

Domain will be all real numbers since no restrictions of x is present.

The range will be [4, +∞), because the minimum value of absolute function is 0

Answer 2

Domain-- All the real numbers.

Range-- [4,∞)

Explanation:

We are given a function f(x) as:

`f(x)=5|x-2|+4`

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:

`|x-2|\geq 0\\\\5|x-2|\geq 0\\\\5|x-2|+4\geq 4\\\\i.e.\\\\f(x)\geq 4`

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

Hence,

Range= [4,∞)