Question

f(x) = x2 + 1 and g(x) = x2 - 1.Step 3 of 3 : Find five ordered pairs that satisfy the sum of the functions, f(x) = x2 + 1 and g(x) = x2 – 1.AnswerHow to enter your answer (Opens in new window){O, O)(OO)(O)(O)(OO)}

Answer 1

The ordered pairs that satisfy the functions
`f(x) = x^2 + 1` and
`g(x) = x^2 - 1`are: (0, 1), (1, 2), (-1, 2), (2, 5), (-2, 5) for f(x), (0, -1), (1, 0), (-1, 0), (2, 3), (-2, 3) for g(x), and (0, 0), (1, 2), (-1, 2), (2, 8), (-2, 8) for f(x) + g(x).

The given functions are
`f(x) = x^2 + 1 and g(x) = x^2 - 1.`

To find ordered pairs that satisfy these functions, we can substitute different values of x and calculate the corresponding y values.

For f(x):

When x = 0, f(0) = 0^2 + 1 = 1, so we have the ordered pair (0, 1).

When x = 1, f(1) = 1^2 + 1 = 2, so we have the ordered pair (1, 2).

When x = -1, f(-1) = (-1)^2 + 1 = 2, so we have the ordered pair (-1, 2).

When x = 2, f(2) = 2^2 + 1 = 5, so we have the ordered pair (2, 5).

When x = -2, f(-2) = (-2)^2 + 1 = 5, so we have the ordered pair (-2, 5).

For g(x):

When x = 0, g(0) = 0^2 - 1 = -1, so we have the ordered pair (0, -1).

When x = 1, g(1) = 1^2 - 1 = 0, so we have the ordered pair (1, 0).

When x = -1, g(-1) = (-1)^2 - 1 = 0, so we have the ordered pair (-1, 0).

When x = 2, g(2) = 2^2 - 1 = 3, so we have the ordered pair (2, 3).

When x = -2, g(-2) = (-2)^2 - 1 = 3, so we have the ordered pair (-2, 3).

For f(x) + g(x):

Adding the corresponding y values from f(x) and g(x) for each x value, we get the following ordered pairs:

When x = 0, f(0) + g(0) = 1 + (-1) = 0, so we have the ordered pair (0, 0).

When x = 1, f(1) + g(1) = 2 + 0 = 2, so we have the ordered pair (1, 2).

When x = -1, f(-1) + g(-1) = 2 + 0 = 2, so we have the ordered pair (-1, 2).

When x = 2, f(2) + g(2) = 5 + 3 = 8, so we have the ordered pair (2, 8).

When x = -2, f(-2) + g(-2) = 5 + 3 = 8, so we have the ordered pair (-2, 8).

Answer 2

`\left(-1,2\right),(0,0),(1,2),(2,8),(3,18)`

1) To find five ordered pairs that satisfy the sum of functions f(x)=x²+1 and g(x)=x²-1 let's add these functions:

2) Let's set a t-table for 5 points that are in the f(x) function:

So, here it goes 5 points for f(x) (-1,2), (0,1), (1,2), (2,5), (3,10)

3) Now for g(x)=x²-1, as in step 2

(-1,0), (0,-1), (1,0), (2,3), (3,8)

4) And finally, the five ordered pairs the sum of f(x) and g(x):

`\begin{gathered} (f+g)(x)=x^2-1+x^2+1 \\ (f+g)(x)=2x^2 \end{gathered}`

(-1, 2), (0,0), (1,2), (2,8), (3,18)