. Fill in the table for 𝑓(𝑥) and 𝑔(𝑥).𝒇(𝒙) = 𝒙^2 𝒈(𝒙) = (𝒙 − 𝟏)^2-2

Question

−2
−1
0
1
2
Show mathematically how you found any one of
values in the last column of the table above

Answer 1

To find the value of a function, we substitute the given value of x into the function and evaluate the expression.

Let's calculate the value of f(x) when x = 1:
f(x) = x^2
f(1) = 1^2
f(1) = 1

So, f(1) = 1.

We can also calculate the value of g(x) when x = 1:
g(x) = (x - 1)^2 - 2
g(1) = (1 - 1)^2 - 2
g(1) = 0^2 - 2
g(1) = -2

So, g(1) = -2.

We can then fill in the table as follows:

x | f(x) | g(x)
-----------------
-2 | 4 |
-1 | 1 |
0 | 0 |
1 | 1 | -2
2 | 4 |

Remember to perform similar calculations for the remaining values of x to fill in the table completely.