For f of x equals the quotient of the quantity 1 minus x and the quantity 1 plus x and g of x equals the quotient of the quantity x and the quantity 1 plus x, find the simplified form for f [g(x)] and state the domain.

Answer 1

why all the wordy mumbo jumbo? Ever heard of math symbols?

f(x) = (1-x)/(1+x)
g(x) = x/(1+x)

f(g) = (1-g)/(1+g)
= (1-(x/(1+x)))/(1+(x/(1+x)))
= 1/(2x+1)

the domain excludes x = -1, since g is not defined there. It also exludes x = -1/2, as shown by the final form of the fraction.

Answer 2

f(x)=(1-x)/(1+x)

g(x)=x/(1+x)

f(g(x))=(1-[x/(1+x)])/(1+[x/1+x])

f(g(x))=((1+x-x)/(1+x)/((1+x+x)/(1+x))

f(g(x))=(1/(1+x))*(1+x)/(1+2x)

f(g(x()=1/(1+2x)

the domain is all real numbers except any number that makes the denominator equal to 0

so, 1+2x=0, 2x=-1, x=-1/2

the domain is all real numbers except -1/2