Question

is f(x)+g(x) equal to 3x^2+x−1

Answer 1

Let f(x)=2x^2+5x−3, g(x)=x^2−4x+2, and h(x)=−x^2+4x−2. Select all of the expressions that are equivalent to 3x^2+x−1.

Answer 2

We cannot determine if f(x)+g(x) is equal to 3x^2+x-1 without knowing the functions f(x) and g(x). Can you provide the functions f(x) and g(x) for further analysis?

Answer 3

To find out which expressions are equivalent to 3x^2 + x - 1, we can combine the given functions f(x), g(x), and h(x) in different combinations and check if any of them are equal to 3x^2 + x - 1.

Let's try the following combinations:

1. (f(x) + g(x))
f(x) = 2x^2 + 5x - 3
g(x) = x^2 - 4x + 2
f(x) + g(x) = 2x^2 + 5x - 3 + x^2 - 4x + 2 = 3x^2 + x - 1

So, f(x) + g(x) is equivalent to 3x^2 + x - 1.

Now, let's check the other combinations:

2. (f(x) + h(x))
f(x) = 2x^2 + 5x - 3
h(x) = -x^2 + 4x - 2
f(x) + h(x) = 2x^2 + 5x - 3 - x^2 + 4x - 2 = x^2 + 9x - 5

3. (g(x) + h(x))
g(x) = x^2 - 4x + 2
h(x) = -x^2 + 4x - 2
g(x) + h(x) = x^2 - 4x + 2 - x^2 + 4x - 2 = 0

Based on our analysis, only the expression f(x) + g(x) is equivalent to 3x^2 + x - 1.