Solve g(x) = -x + 4: Finding Where f(x) < g(x) Using Graphs

The following function is graphed below:

$g(x)=-x+4$

For which values of x is

$f(x) < g(x)$ true?

To solve this problem, we start by analyzing the graph of both functions. The line $g(x) = -x + 4$ and a parabola $f(x)$ intersect at points labeled $B$ and $C$. We observe the behavior of these functions within the interval determined by these intersection points.

• Step 1: Identify intersection points from the graph. Points $B(4,0)$ and $C(1,3)$ are where $g(x)$ is equal to $f(x)$.
• Step 2: Analyze the graph to establish where $f(x) < g(x)$ occurs. From the graph, this occurs when the parabola (representing $f(x)$) is below the line $g(x) = -x + 4$.
• Step 3: The region where $f(x)$ is below $g(x)$ is between the points of intersection. On the graph, this is between $x = 1$ and $x = 4$.

Therefore, the solution is within the interval $1 < x < 4$, during which $f(x) < g(x)$.

Thus, the solution to the problem is $1 < x < 4$.