Question

The table gives values of the function f for selected values of x. The function g is given by g(x) = x^2. Which of the following gives values of g(f(x)) for x= -1, x=0, and x=1?

Answer 1

Answer:

  C

Step-by-step explanation:

You want the table that represents g(f(x)) for g(x) = x², and f is the relation {(-1, 0), (0, 1), (1, -1)}.

G(x)

Squaring the values of f(x) will give you the appropriate values of g(f(x)).

  (-1, 0²) = (-1, 0)

  (0, 1²) = (0, 1)

  (1, (-1)²) = (1, 1)

The g(f(x)) values 0, 1, 1 match those in Table C.

Answer 2

Sure, I can help you with this.

The table shows the values of the function f for x = -1, 0, and 1. We are given that g(x) = x^2 and asked to find the values of g(f(x)) for the same three values of x.

To find g(f(x)), we need to first find the value of f(x) for each given value of x. Then, we can square that value to find g(f(x)).

Here's how to do it:

1. **For x = -1:**

   * From the table, f(-1) = 0.

   * Therefore, g(f(-1)) = g(0) = 0^2 = 0.

2. **For x = 0:**

   * From the table, f(0) = 1.

   * Therefore, g(f(0)) = g(1) = 1^2 = 1.

3. **For x = 1:**

   * From the table, f(1) = -1.

   * Therefore, g(f(1)) = g(-1) = (-1)^2 = 1.

Therefore, the values of g(f(x)) for x = -1, x = 0, and x = 1 are 0, 1, and 1, respectively.

So the answer is the **second option**:

```

g(f(x)) = 0, 1, 1

```