x) and g(x) are linear polynomial functions such that for all x€R fog=Gof=I and f(0)=4 and g(5)=10 then value of f(50)

Since the question says  both f (x) and g (x) are linear polynomial functions,we know that the highest degree of

the function is going to be 1.

Let's assume f (x)=ax+b,where a and b are unknown constants.

Now,the second  condition is just saying that g (x) is the inverse of the function f (x)(since f(g(x))=x=g(f(x)) is only possible when g(x)=f^-1(x)  )So,g(x) comes out to be : g(x)=(x-b)/a 

Now,the last two conditions can be used to find out the values of a and b.

Condition 1:f(0)=b=4, so b is 4

Condition 2:g(5)=(5-4)/a is 10,which gives a to be 1/10 

Now,we know f(x)=0.1x + 4

And thus f(5)=9