We are given the equation $f(x) = -x + 3$ and asked to solve for $x$ when $f(x) = 4$.

Step-by-step solution:

1. Start with the given function: $f(x) = -x + 3$

2. Substitute $f(x) = 4$ into the equation: $4 = -x + 3$

3. Solve for $x$:

   • Subtract 3 from both sides: $4 - 3 = -x$ $1 = -x$

   • Multiply both sides by -1: $x = -1$

Thus, $x = -1$.

Final answer:

$x = -1$.

Would you like more details, or do you have any questions?

Here are 5 related questions to expand your understanding:

1. What happens if we change $f(x)$ to a quadratic function?
2. How would you solve $f(x) = -x + 5$ when $f(x) = 6$?
3. What is the domain and range of the function $f(x) = -x + 3$?
4. How do we interpret the slope and intercept of the linear function $f(x) = -x + 3$?
5. Can you express $x$ in terms of $f(x)$ from $f(x) = -x + 3$?

Tip: When solving linear equations, isolating the variable is key. Simplify the equation step by step!