Question

Please help I don’t understand this

Answer 1

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.

  $\displaystyle\left(\frac{g}{f}\right)(x)=\frac{g(x)}{f(x)}=\frac{\sqrt{x-1}}{\sqrt{x^2-1}}=\sqrt{\frac{x-1}{x^2-1}}$

At this point, you're supposed to know the factoring of the difference of squares:

  $\displaystyle=\sqrt{\frac{x-1}{(x-1)(x+1)}}=\boxed{\sqrt{\frac{1}{x+1}}}$