Questions: f(x)=x-5 g(x)=-x+1

Transcript text: $\left\{\begin{array}{c}f(x)=x-5 \\ g(x)=-x+1\end{array}\right.$

Solution

Solution Steps

To find the point of intersection of the two functions $ f(x) = x - 5 $ and $ g(x) = -x + 1 $, we need to set the two equations equal to each other and solve for $ x $. Once we have the $ x $-coordinate, we can substitute it back into either function to find the corresponding $ y $-coordinate.

Step 1: Set the Functions Equal

To find the point of intersection of the functions $ f(x) = x - 5 $ and $ g(x) = -x + 1 $, we set them equal to each other: \[ x - 5 = -x + 1 \]

Step 2: Solve for $ x $

Rearranging the equation gives: \[ x + x = 1 + 5 \] \[ 2x = 6 \] Dividing both sides by 2, we find: \[ x = 3 \]

Step 3: Find the Corresponding $ y $-Coordinate

Substituting $ x = 3 $ back into either function to find $ y $: \[ f(3) = 3 - 5 = -2 \] Thus, the corresponding $ y $-coordinate is $ -2 $.