Compute the indicated value if it exists? (Look in description) precalc

Question

Let f be the function defined by
f={(-3,4),(-2,2),(-1,0),(0,1),(1,3),(2,4),(3,-1)}

And let g be the function defined
g= {(-3,-2),(-2,0),(-1,-4),(0,0),(1,-3),(2,1),(3,2)}

Compute the indicated value if it exists.
51. (f+g)(-3)
53. (fg)(-1)
55. (g-f)(3)
57. (f/g)(-2)

I need help how to get the solution step by step please and I want to know what the name of this specific section.

Answer 1

f(-3) = 4, g(-3) = -2, (f+g)(-3) = 4 + (-2)

f(-1) = 0, g(-1) = -4, (fg)(-1) = 0 · (-4)

g(3) = 2, f(3) = -1, (g - f)(3) = 2 - (-1)

f(-2) = 2, g(-2) = 0, (f/g)(-2) = 2/0 - undefined

Answer 2

For each one, you have a composition of functions.

 

 

I will do the first one for you.

 

51)

 

(f + g)(-3) = f(-3) + g(-3)

 

Take the y-coordinate of function f when x=-3.  You can get it from       f=(-3, 4)

Take the y-coordinate of function g when x=-3.  You can get it from     g=(-3, -2)

 

Add those two y-coordinates together.  That will be (f + g)(-3).

 

 

Do the same process for the others.  I will help you map out the function operations for the others.

 

52)

 

(fg)(-1) = f(-1) * g(-1)

 

 

53)

 

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

 

 

54)

 

(f/g)(-2) = f(-2) / g(-2)