how to find (fog) (x) if it is in fraction

Question

1. f(x)=3x+4/3x-4

g(x)=7x+4/5x-3 

 

Prove that :- f[g(x)]=0

Answer 1

f[g(x)]=0 is to be demonstrated. NOTE: You were careless in preceding this with both : and -, neither of which is helpful.

 

f is assumed to be the rational function having 3x+4 as numerator and 3x - 4 as denominator, BOTH OF WHICH SHOULD HAVE BEEN PARENTHESIZED.  A similar remark applies to g.

 

But in this case, the claim is not true.  When you substitute the g function's rational expression for x everywhere that x appears in the expression for f, you will be required to get a common denominator in two places, i.e. a four storey division problem will arise.  The simplification will not eventually have a zero in the only surviving numerator, and thus cannot be zero.