Question

A function y = g(x) is graphed below. What is the solution to the equation g(x) = 3?

Answer 1

See below.

Explanation:

From the graph, we can see that g(x)=3 is true only when x is between 3 and 5. However, note that when x=3, the point is a closed circle. When x=5, the point is an open circle. Therefore, the solution is between 3 and 5, and it includes 3 but not 5.

In set-builder notation, this is:

`\{x|x\in \mathbb{R}, 3\leq x<5\}`

In interval notation, this is:

`[3,5)`

Essentially, these answers are saying: The solution set for g(x)=3 is all numbers between 3 and 5 including 3 and not including 5.