Consider the functions f(x) = 3x − 2 and g(x) = x2 − 1. What is the value of (f + g)(−4)?

Question

mathstudent55 · Answer

(f + g)(x) = f(x) + g(x)
Evaluate each function at -4 and add the results.

anonymous · Answer

I'm sorry but I don't get what that means. Sorry I am quite bad at Algebra, Geometry is my thing.

mathstudent55 · Answer

To evaluate f(-4), do this:

f(-4) = 3(-4) - 2
Can you finish that now?

Then do the same for g(-4):
g(-4) = (-4)^2 - 1
Can you finish that also?

Then just add what you get for f(-4) and g(-4)

anonymous · Answer

Oh alrighty, so its 1?

mathstudent55 · Answer

f(-4) = 3(-4) - 2 = -12 - 2 = -14

g(-4) = (-4)^2 - 1 = 16 - 1 = 15

f(-4) + g(-4) = -14 + 15 = 1

You are correct.

anonymous · Answer

Awesome thank you! One final question, when for example the equation has f[g(5)] where it is multiplied how do you solve that?

mathstudent55 · Answer

This is not multiplied.
This is first finding the value of g(5), then inserting that value into f(x).

anonymous · Answer

Oh alright that just saved me from getting multiple questions wrong.

mathstudent55 · Answer

The way to show a product of functions is

$ (f \cdot g)(x) = f(x) \cdot g(x)$ 

The following is the composition of functions, which is what you had above:

$ (f \circ g)(x) = f(g(x)) $ 

The line above is read: The composition of function f and function g is function f evaluated at g.