for the given functions f and g, find the requested function and state its domain

Question

f(x)=6x-3 ; g(x)=2x-4

Answer 1

Brenda,

 

Calculating the function is a matter of algebraic operations (addition, subtraction, substitution and division) so I'll let you figure that one out. In this case of domain, we can say it's all real numbers except for f/g because there is a general rule that you cannot divide by zero. So if you divide f/g, you have to exclude all cases where g(x)=0. This means for f/g, it's all x except for when 2x-4=0 or x=2.

 

Hope that helps!

Answer 2

(f+g)(x) = f(x) + g(x) = 6x-3+2x-4 = 8x-7   domain = (-∞, ∞)

 

(fg)(x) = f(x) g(x) = (6x-3)(2x-4) = 12x² - 30x + 12  domain = (-∞,∞)

 

(f-g)(x) = f(x) - g(x) = (6x-3) - (2x - 4) = 4x + 1  domain = (-∞,∞)

 

(f/g)(x) = f(x)/g(x) = (6x-3)/(2x-4)   domain = {x l 2x - 4 ≠ 0}

 

                                                              = {x l x ≠ 2} 

 

                                                              = (-∞, 2) ∪ (2, ∞)

 

(f o g)(x) = f(g(x)) = f(2x-4) = 6(2x-4) -3 = 12x - 27  domain = (-∞,∞)