the functions f and gare defined by

Question

f(x)=2/(x+1), x>0 g(x)=1-x^2, xER
a)find value of fg(x)giving your answer in the simplest form.
b) find f^-1(x)
c) solve f(x)= f^-1(x)

Answer 1

fg(x) is the product of the two functions.
for f(x) = 2/(x+1), x>0 and
g(x) = 1-x², x∈ℝ
fg(x) = (2/(x+1))(1-x²)
=2(1+x)(1-x)/(x+1)
Now, what is the domain of fg(x)?
Can you divide both numerator and denominator by (1+x)? Why or why not?