Question

Please help me with my calc homework, I am paying close attention to the answer

Answer 1

Answer:
`f(g(x))=(1+x)/((1-x)(2x+1))`

The domain is the set of real numbers excluding 1 and -1/2

Step-by-step explanation:

Given the functions:

`\begin{gathered} f(x)=(1-x)/(x+1) \\ \\ g(x)=(x)/(1-x) \end{gathered}`

Then

`\begin{gathered} f(g(x))=(1-(x)/(1-x))/((x)/(1+x)+1) \\ \\ =\frac{(1-x-x)/(1-x)}{\frac{x+1+x_{}}{1+x}}=((1)/(1-x))/((2x+1)/(1+x)) \\ \\ =(1)/(1-x)*(1+x)/(2x+1) \\ \\ =(1+x)/((1-x)(2x+1)) \end{gathered}`

The domain is the set of real numbers excluding 1 and -1/2