help please
For f(x)=3x+1 and g(x)=x^2-6 find (f-g)(x)
A. x^2-3x-7
B. 7+3x-x^2
C. 3x^2-17
D. -x^2+3x-5
To find (f - g)(x), you need to subtract the function g(x) from the function f(x).
Given:
f(x) = 3x + 1
g(x) = x^2 - 6
To subtract g(x) from f(x), you subtract each corresponding term.
(f - g)(x) = f(x) - g(x) = (3x + 1) - (x^2 - 6)
To subtract the two functions, distribute the negative sign to each term in g(x):
= 3x + 1 - x^2 + 6
Now, combine like terms:
= -x^2 + 3x + 7
Therefore, the answer is (D) -x^2 + 3x - 5.