Question

Use the tables to answer the question.

Table 1: f(x)=3x2−1

Table of x and f(x) Values
x f(x)
1 2
2 11
3 26
4 47
Table 2: Inverse of f(x)=3x2−1


Complete the Table for Inverse Function for Corresponding x Values
x f−1(x)
11 2
47 ?
26 3
Using the table of values of the function f(x)=3x2−1
, fill in the missing value in the second table to show the inverse function.

(1 point)
The missing value in the table is
.
Remaining Attempts : 3
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Answer 1

To find the missing value in the inverse function table, we need to determine for which value of \( x \) in the original function \( f(x) = 3x^2 - 1 \) gives \( f(x) = 47 \).

The original function is given by:
\[ f(x) = 3x^2 - 1 \]

We set \( f(x) = 47 \):
\[ 3x^2 - 1 = 47 \]

Now, let's solve for \( x \):
1. Add 1 to both sides:
\[ 3x^2 = 48 \]
2. Divide both sides by 3:
\[ x^2 = 16 \]
3. Take the square root of both sides:
\[ x = 4 \quad \text{or} \quad x = -4 \]

Since we are working with the table that uses positive values of \( x \), we will use \( x = 4 \).

This means that when \( f(x) = 47 \), \( x = 4 \). Therefore, the inverse \( f^{-1}(47) = 4 \).

Now we can complete the table for the inverse function:

| x | f⁻¹(x) |
|----|--------|
| 11 | 2 |
| 47 | 4 |
| 26 | 3 |

Thus, the missing value in the table is **4**.