Question

If f:R->R is given by f(x)=ex and g:R->R is given by g(y)=sin y, find the composite mappings fog and gof

Answer 1

we know, concept of composite function : the function f : A→ B and g : B→ C can be composed to form a function which maps x in A to g(f(x)) in C. A composite function is denoted by (g o f) (x) = g (f(x)).

given, f : R -----> R is given by f(x) = e^x

and g : R ------> R is given by g(y) = siny

it can be written as g : R -----> R is given by, g(x) = sinx

we have to find (fog)(x)

= f(g(x)) = f(sinx)

= e^{sinx}

hence, fog = e^{sinx}

we have to find (gof)(x)

= g(f(x)) = g(e^x)

= sin(e^x)