if f(x) = sin (x) and g(x) = 1/x, then (fg) (x) = sin (1/x) and f(x).g(x) = sin(x)/x.?

Question

Pls explain, how come, (fg) (x)= f(x). g(x)

Answer 1

Assuming you mean to multiple these functions: (fg)(x) = (sin(x))(1/x) = (sin(x))/x but NOT sin(1/x).



Now what do you mean by f(x).g(x)? are you taking their compositions? The composition would be:

f(g(x))=sin(1/x), that is g(x) is the input to f(x), or rather, 1/x is the input to sin(x).



Therefore, in this case, f times g does NOT equal f composition g. I say "in this case" because it is possible that multiplying two functions could turn out to be the same as taking their compositions--although I have never seen an example of that--and I don't feel like trying to make up an example :-)

Answer 2

(fg) (x) means that you take g(x) and put it inside f(x), so (fg) (x) = sin (1/x) or opening brackets will be (sinx) / x.

f(x) g(x) is the same thing = sinx (1/x) = sinx / x.

Conclusion: (fg) (x) = f(x) g(x)



I would say its not (fg) (x), i think its f(g(x)).

Answer 3

one is taking the output of a function and using it as the INput of the next function.



The other is simply multiplying the outputs of each function together.



1st is usally written f(g(x)) and you can see that the INPUT for the f(x) function is now whatever the g(x) OUTPUTS when the input is x! try to reason it through until you say "ahhhhhhhhhhh!"



good luck!

Answer 4

(fg)(x) = f(x) * g(x) = sinx/x . (fog)(x) = f(g(x)) = f(1/x) = sin(1/x)

Answer 5

(fg)(x) is the product function

(fg) (x) is defined as f(x) g(x)



This is not to be confused with (f.g)(x)= f(g(x))

Answer 6

(fg) (x)= f(x). g(x) because f(x) =g(x) = 1/x and x (fg)