Question

If f = (1,2) , (3,4) , (5,6) and g = (2,3) , (4,6) , (6,8) . Find the composite of gof. does fog exist?

Answer 1

Answer:

$g\circ f=\{(1,3),(3,6),(5,8)\}$.

$f\circ g$ does not exist.  

Step-by-step explanation:

It is given that,

$f=\{(1,2),(3,4),(5,6)\}$

$g=\{(2,3),(4,6),(6,8)\}$

We need to find the composition gof.

$(g\circ f)(x)=g(f(x))$

Now,

$(g\circ f)(1)=g(f(1))=g(2)=3$

$(g\circ f)(3)=g(f(3))=g(4)=6$

$(g\circ f)(5)=g(f(5))=g(6)=8$

So, $g\circ f=\{(1,3),(3,6),(5,8)\}$.

We need to check whether $f\circ g$ exist of not.

If range of g(x) is subset of domain of f(x), then we can say composition function $f\circ g$ exists.  

Now,

Range of g(x) = {3,6,8}

Domain of f(x) = {1,3,5}

Since range of g(x) is not a subset of domain of f(x), then we can say composition function $f\circ g$ does not exist.