Is y a function of x or Sine in f(x)=sinx?

[roger]

Hello.

Please can someone help me with this :


f(x)=sinx


For the above, is y a function of x OR is y a function of Sine ?


Secondly, I don't understand what it means by :

a f(x)

and f(ax)

where a is 2.

What I need to know is what does each do to the graph of sin x ?

Also do each of the two af(x) and f(ax) pass the same points on the x-axis as just sinx ?

Please help me


rog

 

[nolachrymose]

For f(x) = sin(x), f is a function of x.
What is meant by af(x) is that the value of f(x) is multiplied by the constant a. The expression f(ax) means that x is multiplied by the constant a, and then function f is applied to that value.
Hope that helps! :)

 

[Galileo]

f(x)=sin(x) is also a function of sin(x).
It depends how you look at it.
If you take y=sin(x), then f(x)=y. So f is clearly a function of y=sin(x).
However, since sin(x) is a function of x, f is also a function of x.

If f were given by: f(x)=sin(x)+x, it would not be a function of sin(x), but only of x.