Let f(x) = 4x – 5 and g(x) = 3x + 7. Find f(x) + g(x) and state its domain.
To find f(x) + g(x), we simply add the two functions together.
f(x) + g(x) = (4x - 5) + (3x + 7)
= 4x - 5 + 3x + 7
= (4x + 3x) + (-5 + 7)
= 7x + 2
So, f(x) + g(x) = 7x + 2.
The domain of f(x) + g(x) is the set of all real numbers, since there are no restrictions on the values of x for which the sum is defined.