Let f(x) = 3x^2 + 2x - 1 and g(x) = x^2 - 3x + 1
Part A: Find f(x) + g(x)
Part B: Find f(x) - g(x)
Part A:
To find f(x) + g(x), we need to add the two functions together:
f(x) + g(x) = (3x^2 + 2x - 1) + (x^2 - 3x + 1)
Combining like terms, we get:
f(x) + g(x) = 3x^2 + x^2 + 2x - 3x - 1 + 1
Simplifying further:
f(x) + g(x) = 4x^2 - x
Therefore, f(x) + g(x) = 4x^2 - x.
Part B:
To find f(x) - g(x), we need to subtract g(x) from f(x):
f(x) - g(x) = (3x^2 + 2x - 1) - (x^2 - 3x + 1)
Distributing the negative sign, we get:
f(x) - g(x) = 3x^2 + 2x - 1 - x^2 + 3x - 1
Combining like terms, we get:
f(x) - g(x) = 3x^2 - x^2 + 2x + 3x - 1 - 1
Simplifying further:
f(x) - g(x) = 2x^2 + 5x - 2
Therefore, f(x) - g(x) = 2x^2 + 5x - 2.