what is the range of f(x)=|x-3|+2?

f(x)=|x-3|+2

Note that |x-3| >= 0 for all real x

|x-3| >= 0

So Now adding 2 on both sides of equality, we get

|x-3| + 2 >= 0 + 2

So |x-3| + 2 >= 2

f(x) >= 2

HENCE this means that range of function f(x) = |x-3| + 2 is all real numbers which are >= 2

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