Question

he table shows values for functions f(x) and g(x) .

x f(x)=3x g(x)=2x+1
−2 19 −3
−1 13 −1
0 1 1
1 3 3
2 9 5
What is the solution to f(x)=g(x) ?

Select each correct answer.



Responses

x = −2
x = − 2

x = −1
x = − 1

x = 0
x = 0

x = 1
x = 1

x = 2

Answer 1

To find the solution to the equation \( f(x) = g(x) \), we can compare the values of \( f(x) \) and \( g(x) \) in the table you provided:

\[
\begin{array}{|c|c|c|}
\hline
x & f(x) = 3x & g(x) = 2x + 1 \\
\hline
-2 & 19 & -3 \\
-1 & 13 & -1 \\
0 & 1 & 1 \\
1 & 3 & 3 \\
2 & 9 & 5 \\
\hline
\end{array}
\]

Let's check each value of \( x \) to see where \( f(x) \) equals \( g(x) \):

- For \( x = -2 \):
- \( f(-2) = 19 \)
- \( g(-2) = -3 \)

- For \( x = -1 \):
- \( f(-1) = 13 \)
- \( g(-1) = -1 \)

- For \( x = 0 \):
- \( f(0) = 1 \)
- \( g(0) = 1 \)
- \( \Rightarrow f(0) = g(0) \) (this is a solution)

- For \( x = 1 \):
- \( f(1) = 3 \)
- \( g(1) = 3 \)
- \( \Rightarrow f(1) = g(1) \) (this is a solution)

- For \( x = 2 \):
- \( f(2) = 9 \)
- \( g(2) = 5 \)

The solutions to the equation \( f(x) = g(x) \) are:

- \( x = 0 \)
- \( x = 1 \)

So the correct answers are:

- \( x = 0 \)
- \( x = 1 \)