Answer:
d. √(1/(x+1))
Step-by-step explanation:
Just as operations can be performed on numbers and variables, so can operations be performed on functions. Here, you're asked to simplify the ratio of two functions.
[tex]\displaystyle\left(\frac{g}{f}\right)(x)=\frac{g(x)}{f(x)}=\frac{\sqrt{x-1}}{\sqrt{x^2-1}}=\sqrt{\frac{x-1}{x^2-1}}[/tex]
At this point, you're supposed to know the factoring of the difference of squares:
[tex]\displaystyle=\sqrt{\frac{x-1}{(x-1)(x+1)}}=\boxed{\sqrt{\frac{1}{x+1}}}[/tex]
