If f(x)= x2 + 2x - 6 and g(x)= 3x2 - 5x - 7, find f(x)-g(x).
A) -2x2 - 3x + 1
B) -2x2 + 7x + 1
C) -2x2 - 3x - 13 <my choice
D) 4x2 - 3x - 13
To find f(x) - g(x), we subtract the functions f(x) and g(x) term by term.
f(x) = x^2 + 2x - 6
g(x) = 3x^2 - 5x - 7
To subtract the functions, we subtract the corresponding terms:
f(x) - g(x) = (x^2 + 2x - 6) - (3x^2 - 5x - 7)
Now, let's distribute the negative sign:
f(x) - g(x) = x^2 + 2x - 6 - 3x^2 + 5x + 7
Next, let's combine like terms:
f(x) - g(x) = (x^2 - 3x^2) + (2x + 5x) + (-6 + 7)
Simplifying further:
f(x) - g(x) = -2x^2 + 7x + 1
Therefore, the correct answer is option B) -2x^2 + 7x + 1.
To find the expression f(x) - g(x), you need to subtract g(x) from f(x).
Let's start by subtracting the respective terms of the two functions:
f(x) = x^2 + 2x - 6
g(x) = 3x^2 - 5x - 7
Subtracting g(x) from f(x) gives:
f(x) - g(x) = (x^2 + 2x - 6) - (3x^2 - 5x - 7)
Distribute the negative sign in front of g(x):
= x^2 + 2x - 6 - 3x^2 + 5x + 7
Combine like terms:
= (-3x^2 + x^2) + (2x + 5x) + (-6 + 7)
Simplify further:
= -2x^2 + 7x + 1
Therefore, the correct answer is B) -2x^2 + 7x + 1.
f(x)-g(x)
= (x^2+2x-6)-(3x^2-5x-7)
= x^2+2x-6-3x^2+5x+7
= -2x^2+7x+1
watch those minus signs when subtracting!