Let fx 7x gx 2x1x3 Find g of f and its domainSolutionfx 7x

Let f(x)= 7/x , g(x) = (2x+1)/(x-3)

Find g of f and its domain.

f(x)= 7/x , g(x) = (2x+1)/(x-3)

(g o f)(x): Plug x = f(x) in g(x)

(g o f) (x) = (2*7/x +1)/ (7/x -3)

=(14 +x)/ (7 - 3x)

Domain : denominator should not be zero: so, 7- 3x =0

x = 7/3

So, domian = ( -inf, 7/3) U ( 7/3, inf)