For the given functions f and​ g, complete parts​ (a)-(h). For parts​ (a)-(d), also find the domain.

Question

f(x) = 5x+4; g(x) = 3x-2.

(a) Find (f+g) (x). (f+g) (x) = (Simplify your answer.)

Answer 1

For a problem like this, all we need to do is add the functions together. You can think of the notation like this,

(f+g)(x) = f(x) + g(x)

So, we can plug in f(x) and g(x)

(f+g)(x) = (5x+4) + (3x-2)

Now simplify by combining like terms,

(f+g)(x) = 8x - 2

To find the domain, we need to consider "What are all of the possible values of x that would give us a defined output?"

In this case, we can input any value for x and still receive a defined output for (f+g)(x). Therefore the domain is all real numbers. In interval notation, (-∞,∞).