Question

What is the range of g(x)?

Answer 1

Answer:

$h(x) \leq 5$

Step-by-step 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]

$h(x) \leq 5$