Question

Q. 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

Answer:

fog = e^sin(x) and gof = sin(e^x).

Explanation:

It is given that f(x) = e^x  and g(y) = sin(y)

Composite function/ relation is defined as composing one function / relation / mapping onto another function / relation / mapping.

In relations, composite function fog is defined as

fog = f(g(x))

since g(x) = sin(x), we can substitute

fog = f(sin(x)) = e^sin(x).

Similarly gof is defined as

gof = g(f(x))

since f(x) = e^x, we can substitute

gof = g(e^x)) = sin(e^x)

Hence fog = e^sin(x) and gof = sin(e^x).

Answer 2

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)