For each set of ordered pairs, find fog and gof if they exist, f = {(1,1)(0,-3)} and g = {(1,0)(-3,1)(2,1)},?

Question

Please show all the steps

Answer 1

f = {(1, 1),(0, -3)}
g = {(1, 0), (-3, 1), (2, 1)}

This tells us that
f(1) = 1
f(0) = -3

g(1) = 0
g(-3) = 1
g(2) = 1

Therefore, we want to find: fog(1), fog(-3), fog(2)

(fog)(1) = f(g(1)) = f(0) = -3
(fog)(-3) = f(g(-3)) = f(1) = 1
(fog)(2) = f(g(2)) = f(1) = 1

We also want to find gof(1), gof(0)

gof(1) = g(f(1)) = g(1) = 0
gof(0) = g(f(0)) = g(-3) = 1

Answer 2

Here
f = {(1, 1),(0, -3)}
g = {(1, 0), (-3, 1), (2, 1)}

This means
f(1) = 1, f(0) = -3 and g(1) = 0, g(-3) = 1, g(2) = 1
Now,
Find the value of gof(1), gof(0)
gof (1) = g(f(1)) = g(1) = 0
gof (0) = g(f(0)) = g(-3) = 1
Also
Find the value of fog(1), fog(-3), fog(2)
fog (1) = f(g(1)) = f(0) = -3
fog (-3) = f(g(-3)) = f(1) = 1
fog (2) = f(g(2)) = f(1) = 1

Answer 3

f = {(1,1), (0,-3)}
g = {(1,0), (-3,1), (2,1)}

For fog we need to apply f to every element of g:
fog = {(1, f(0)), (-3, f(1)), (-2, f(1))}
= {(1, -3), (-3, 1), (-2, 1)}

Similarly we get
gof = {(1, g(1)), (0, g(-3))}
= {(1, 0), (0, 1)}

Answer 4

f = {(0,0), (4, -2)}
g = {(0,4), (-2,0), (5,0)}

Answer 5

They will not exist as g is not a function

Answer 6

Go with Puggy, not Scarlet Manuka. I assure you, Puggy's answer is perfect. (No, he's not my pal -- I don't know him).