The values in the table define the function *f*(*x*). If *g*(*x*) is the inverse of *f*(*x*), what is the value of *g*(1)?


*xf*(*x*)

-1

-3

1

-1

4

1

6

4

7

6

 **A.** 

1

 **B.** 

2

 **C.** 

3

 **D.** 

4

 **E.** 

5

To solve for \( g(1) \), where \( g(x) \) is the inverse of \( f(x) \), we need to recall that if \( g(x) \) is the inverse of \( f(x) \), then:

\[
g(f(x)) = x \quad \text{and} \quad f(g(x)) = x
\]

This means that \( g(1) \) is the \( x \)-value such that \( f(x) = 1 \).

From the table of \( f(x) \):

\[
\begin{aligned}
f(-1) &= -3 \\
f(1) &= -1 \\
f(4) &= 1 \\
f(6) &= 4 \\
f(7) &= 6
\end{aligned}
\]

We can see that \( f(4) = 1 \). Therefore, \( g(1) = 4 \).

Thus, the value of \( g(1) \) is:

\[
\boxed{4}
\]

Would you like a detailed breakdown or have any further questions?

Here are 5 related questions for practice:

1. If \( f(x) = -1 \), what is \( g(-1) \)?
2. Find \( f(g(4)) \) using the table.
3. If \( h(x) \) is the inverse of \( g(x) \), what is the value of \( h(4) \)?
4. For what value of \( x \) does \( f(x) = -3 \)?
5. Can you determine \( g(-3) \) from the table?

**Tip:** For inverse functions, always swap the input and output values of the original function.

The values in the table define the function f(x). If g(x) is the inverse of f(x), what is the value of g(1)?

|x | f(x)|
|---|----|
|-1 | -3 |
| 1 | -1 |
| 4 | 1  |
| 6 | 4  |
| 7 | 6  |

**A.** 1 **B.** 2 **C.** 3 **D.** 4 **E.** 5

This problem helps you find the value of g(1), where g(x) is the inverse of f(x), by using a table of function values. Explore the concept of inverse functions, and learn how to solve for unknown values using function properties. Ideal for students in Grades 8-10.

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