Annie T. answered • 03/06/23
Mathematics Teacher Tutoring from Pre-Algebra to Calculus
Consider the following functions. f(x) = x − 3, g(x) = x^2
A) Find (f+ g)(x) :
(f + g)(x) = f(x) + g(x) = (x − 3) + (x^2) = x^2 + x − 3
B)Find the domain of (f+ g)(x).
The domain of (f + g)(x) is the intersection of the domain of f(x) and g(x). Since f(x) is a linear function and g(x) is a quadratic function, their domains are all real numbers, (-∞,∞). So the domain of (f+g)(x) is (-∞,∞).
C)Find (f − g)(x).
(f − g)(x) = f(x) − g(x) = (x − 3) − (x^2) = -x^2 + x − 3
D)Find the domain of (f − g)(x)
The domain of (f − g)(x) is the same as the domain of (f + g)(x) , so (-∞,∞).
E)Find (fg)(x).
(fg)(x) = f(x) · g(x) = (x − 3)(x^2) = x^3 − 3x^2
F)Find the domain of (fg)(x)
The domain of (fg)(x) is the same as the domain of (f + g)(x) , so (-∞,∞).
G)Find (f/g)(x)
(f/g)(x) = f(x)/g(x) = (x − 3)/x^2
E) Find the domain of (f/g)(x)
The domain of (f/g)(x) is the same as the domain of (f + g)(x) with the added restriction that g(x)≠0. Since g(x) ≠ 0 is x^2 ≠ 0, this means that x ≠ 0. So the domain of (f/g)(x) is (-∞,0)∪(0,∞).
