Operations on Function, teach me, please.?

Question

Help me, I don't know how to do this.
Using the values of the functions f and g given below.
x f(x)
1 3
2 5
3 1
4 2
5 3

x g(x)
1 5
2 4
3 4
4 3
5 2


Complete the given tables. How to calculate this table?
x (g。f) (x)
1 4
2 ?
3 5
4 ?
5 ?

Answer 1

These are composite functions. Think of them as two step fucntions. And work them from the inside out. The value of
f(x) becomes the input for g(x).

(g◦f)(x) = g[f(x)]

(g◦f)(1) = g[f(1)] = g[3] = 4
(g◦f)(2) = g[f(2)] = g[5] = 2
(g◦f)(3) = g[f(3)] = g[1] = 5
(g◦f)(4) = g[f(4)] = g[2] = 4
(g◦f)(5) = g[f(5)] = g[3] = 4

Answer 2

you may think of of purposes as equations that are represented by way of variables. extremely than n representing a cost, n(x) represents an equation. we could persist with this on your purposes. f(6) = 7here is why: f(x) = x + a million f(6) = 6 + a million f(6) = 7 a similar could be carried out with g(6): g(x) = 2x g(6) = 2*6 g(6) = 12 so, by means of fact f(x) represents x+a million and g(x) represents 2x h(x) could be written as h(x) = (x+a million)+(2x) h(x) = x + a million + 2x h(x) = 3x + a million you're merely plugging in an equation as though it have been a variable right that's a thank you to examine your artwork: f(6) = 7 g(6) = 12 f(6) + g(6) = 19 h(6) = 3*6 + a million h(6) = 18 + a million h(6) = 19 f(6) + g(6) = h(6) = 19 desire this enables, and robust success graduating. i'm going to be on your footwear next year (i'm a junior).

Answer 3

I prefer the notation g(y)=g(f(x))

So, when x=1, f(x)=3, which gives g(3), which gives 4.

And when x=2, f(x)=5, g(5) =2

Get the idea?

Another example, when x= 5, f(x)=3, g(3)=4

Answer 4

So in the first case, find x=1 in the first table, you find that f=3... now find x=3 in the second table, you find that g=4 so g(f(1)) = 4
to check, look at 3..
find x=3 in the first table, you find that f=1... now find x=1 in the second table, you find that g = 5. so g(f(3))=5
now, try 2
find x=2 in the first table, you find that f=5... now find x=5 in the second table, you find that g=2. so g(f(2) = 2
try 4...
find x=4 in the first table, you find that f=2... now find x=2 in the second table, you find that g=4.. so g(f(4))=4

have a bash at 5 on your own...