Question

The function fog exists for the functions f and g , defined by

f(x)= sin t, t∈ R

g(x,y)= x^2+ 5xy + y^2, (x,y)∈ R^2

True or false with full explanation

Answer 1

The given statement is TRue-

Explanation:

As the function f(x) depends upon the variable t, It does not depends upon x.

Also $g(x,y)=x^2+5xy+y^2$

Since There is no relation between x and t , t is independent of x

Therefore sint is independent of x.

Hence sint is constant.

When we calculate-

$fog=f(x^2+5xy+y^2)=sint$

Since in function f(x), Output does not depend upon input x, So Value of fog is sint, Where $t\in R$ Which is a finite quantity, So fog exists.