Solving g(x)=-x+4 > 0: Linear Function Inequality Analysis

Look at the graph below of the following functions:

$f(x)=x^2-6x+8$

$g(x)=-x+4$

For which values of x is
$g(x)>0$ true?

To solve the problem of finding for which values of $x$, the function $g(x) = -x + 4$ is greater than zero, we begin as follows:

• Step 1: Set up the inequality $g(x) > 0$. This translates to $-x + 4 > 0$.
• Step 2: Solve the inequality:
  • Subtract 4 from both sides: $-x > -4$.
  • Multiply both sides by $-1$, reversing the inequality: $x < 4$.

Therefore, the solution to the problem is that $g(x) > 0$ when $x < 4$.

The corresponding choice that reflects this solution is choice 4: $x < 4$.