What is (f+g)(x)?
f(x)=x^2−36
g(x)=x^3+2x^2−10
This answers this question and the next:
(f + g)(x) means that you have to add both f(x) and g(x).
(f + g)(x) = x^2 − 36 + x^3 + 2x^2 − 10
(You have to simplify this)
Similarly,
(f * g)(x) means that you have to multiply f(x) and g(x).
To find (f+g)(x), we need to add the two functions f(x) and g(x) together.
First, let's write down the expressions for f(x) and g(x):
f(x) = x^2 - 36
g(x) = x^3 + 2x^2 - 10
Now, we can add the two functions together:
(f+g)(x) = f(x) + g(x)
Substituting the expressions for f(x) and g(x):
(f+g)(x) = (x^2 - 36) + (x^3 + 2x^2 - 10)
Combining like terms, we get:
(f+g)(x) = x^3 + x^2 - 36 + 2x^2 - 10
Further simplifying:
(f+g)(x) = x^3 + 3x^2 - 46
Therefore, (f+g)(x) is equal to x^3 + 3x^2 - 46.