I'm having a hard time understanding functions and am going through some practice questions but am very confused

Question

Let f (x) = 4x^2 + 2x – 8 and g(x) = 1 – 2x.

(a) Evaluate the function g – f for x = –3. That is, find (g – f)(–3). 

 

(b) Evaluate the function fg for x = –3. That is, find (f g)( –3). 

(c) Find the difference function (f – g)(x) and simplify the results. 

Answer 1

(a)  and (c)

g-f is just g(x)-f(x) for any x

So (g-f)(x) = g(x)-f(x) = 1-2x - (4x^2 +2x -8) = 1-2x-4x^2-2x+8 = -4x^2 -4x +9 

so when x=-3 you can get the number by plugging it in the above equation.

(f-g)(x) = 4x^2 +4x -9 (negative of g-f). 

 

 

(b) fg is product of g(x) and f(x) (unless there is a circle between f and g, which means composition of two functions).

so f(x)g(x) at x=-3  

is f(-3)g(-3) = (36-6-8)*(1+6) = 24*7 = 168

 

Answer 2

f(c) means to evaluate f(x) when x=c.

g(c) means to evaluate g(x) when x=c.

 

 

a)

 

We are subtracting the functions after they have been evaluated.

 

(g - f)(x) = g(-3) - f(-3)

 

 

b)

 

We are multiplying the functions after they have been evaluated.

 

(f g)(-3) = f(-3) * g(-3)

 

 

c)

 

Subtract the general functions.  No evaluation needed.

 

(f - g)(x) = f(x) - g(x)