given that f(x)=x^5+13x and g(x)=8-x find the domain of (f+g)

Question

Need some help solving this problem and finding the domain

 

Answer 1

(f+g)(x) just means add f(x) and g(x) together:

 

(f+g)(x) = f(x) + g(x) = (x⁵ + 13x) + (8 - x) = x⁵ + 13x + 8 - x = x⁵ + 12x + 8

 

 

Finding the domain of a function requires you to figure out what values you can plug in for x. You'll want to make sure none of your x-values force you to divide by zero, take the square root of a negative number, etc. Here, there's nothing to worry about, so you can plug any value in for x. That means your domain is x = all real numbers, which can also be written as {x | -infinity < x < infinity}, -infinity < x < infinity, or (-infinity, infinity).