Question

Create two functions and their intersection points what to functions can be used to solve the following equation 10 - x equals x + 4

Answer 1

To solve the equation \( 10 - x = x + 4 \), we can rewrite it in terms of two functions. Let's define the two functions as follows:

1. \( f(x) = 10 - x \)
2. \( g(x) = x + 4 \)

The intersection points of the two functions can be found by setting \( f(x) \) equal to \( g(x) \):

\[
10 - x = x + 4
\]

Now, we can solve for \( x \):

1. Add \( x \) to both sides:
\[
10 = 2x + 4
\]

2. Subtract 4 from both sides:
\[
6 = 2x
\]

3. Divide by 2:
\[
x = 3
\]

Now that we have \( x = 3 \), we can find the corresponding \( y \)-value by plugging \( x \) back into either function. Let's use \( f(x) \):

\[
f(3) = 10 - 3 = 7
\]

Thus, the intersection point of the two functions is:

\[
(3, 7)
\]

In summary, the two functions \( f(x) = 10 - x \) and \( g(x) = x + 4 \) intersect at the point \( (3, 7) \).