A composition is, in essence, applying one function after another (to form a "chain of functions"). From a symbolic/algebraic perspective, you are "plugging one function into the other".
In precalculus-related courses, when we write #f(g(x))#, the notation means to first apply the function #g# to the number #x# to get the number #g(x)#, then apply the function #f# to the number #g(x)# to get #f(g(x))# (so we work "from inside out"). (In some other math courses, the inputs and outputs don't have to be numbers).
For the function #k(x)=e^(sin(x))#, when a number #x# is substituted, the sine function must be evaluated first to get the number #sin(x)#. This number then must be made the power of #e# to get the final output #e^(sin(x))#. Therefore, the sine function must be the "inner" (first applied) function and the exponential function must be the "outer" (second applied) function.
Hence, #k(x)=f(g(x))# when #f(x)=e^(x)# and #g(x)=sin(x)#.
Extra Info (ignore this at the moment if it's confusing): An alternative notation for this is to use the "circle operator" and write #k(x)=(f circ g)(x)#. This can also be written as #k=f circ g#, which emphasizes that #circ# is a "binary operator" that takes two given functions #f# and #g# and creates a new function #f circ g#. In general, the circle operator #circ# is not commutative (that is, in general, #f circ g != g circ f#. For the present example, these are indeed not equal because #e^(sin(x)) !=sin(e^(x))# as functions (though their graphs do cross each other). Order of operations matters!
