help please with equation. I am not sure where the g came from in algebra.

Question

Can someone teach me how to do this? I just figured out the f(x) in algebra and now there is g? it is entirely confusing and I am not really sure how to solve questions like this. Please teach me how to solve questions like this so I can understand in the future. This just does not make sense.

 

Let f (x) = 5x2 – 7x + 8 and g(x) = 1 – 3x.

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

(b) Find (g – f)(–1).

(c) Find (f g)( –1).

Answer 1

Lindsay,

 

You know that f(x) represents a function.  g(x) just represents another function.

 

a)

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

(f-g)(x) = (5x²-7x+8) - (1-3x)

Now simplify

(f-g)(x) = 5x²-4x+7

 

b) (g-f)(-1) = g(-1) - f(-1)

(g-f)(-1) = [1-3(-1)] - [5(-1)²-7(-1)+8]

(g-f)(-1) = [1+3] - [5+7+8] = 4 - 20 = -16

 

c) (f g)(-1)

I'm going to assume the expression is really (fºg)(-1)

Let's first look at (fºg)(x)

(fºg)(x) = f(g(-1))

This means evaluate g(x) at x = -1.  Then take that answer and make it your x to evaluate f(x).  

g(-1) = 1-3(-1) = 1+3 = 4

f(4) = 5(4)² - 7(4) + 8 

f(4) = 5(16) -28 + 8

f(4) = 80-28+8

f(4) = 60

 

Hope this has helped.

Answer 2

Yes, it is a bit confusing

 

f and g are really just two different functions.

 

(f - g)(x)  means subtract g from f  and is the same as f(x) - g(x)

 

Using the actual functions:

 

(5x2 – 7x + 8) - (1 – 3x)

 

Simplify this to get the answer to "a"

 

For "b", you subtract f from g and then substitute -1 for x

 

For "c" you have to multiply the two functions