math problem I dont get

Question

Given that f(x)=31x/x+19 and g(x)=cot(21x) ,

find f∘g]

1)  xcot(21x)/31x+19

2)  cot(615x/x+19)

3) 31cot(21x)/cot(21x)+19

4) 31cot(21x)/cot(21x)+19

please help me I do not get this

Answer 1

For fºg you take the definition of f, and replace x by g(x), [ so you replace the x by cot (21x) ].

That's all you have to do.

Answer 2

Here is a simpler version of what is required.

Suppose f(x) = 10x² and g(x) = sin x

f º g (x) is notation for f[g(x)]. (composition of functions).

If I asked you what is f(⊗) the answer would be 10(⊗)².

Following that pattern f[g(x)] means to pass g(x) to the f function.

So, f(sin x) = 10(sinx)².

For your problem you are passing cot(21x) into the f function. So wherever you see an "x" in the f function, replace that "x" with cot(21x).

The graphs of these functions are fairly ugly, but after you think you've got it by trying the above suggestions take a look here:

desmos.com/calculator/ivwjd8xjic