Question

What is the range of g(x)?

Answer 1

`h(x) \leq 5`

Explanation:

we know that

1) For x < 3

`h(x)=x+2` ----> is an increasing function

so

For x=3

`h(3)=3+2=5`

But remember that the value of x=3 is not included in this interval

therefore

The range is the interval (-∞,5)

2) For x≥3

`h(x)=-x+8` ---> is a decreasing function

so

For x=3

`h(3)=-3+8=5`

The range is the interval (-∞,5]

therefore

The range of the function h(x) is the interval (-∞,5]

`h(x) \leq 5`