Question

Help me what is the answer?!

Answer 1

Answer:

Hence choice A is correct

Step-by-step explanation:

Given equations are $f(x)=\sqrt{x^2-1}$ and $g(x)=\sqrt{x-1}$

Now we need to find the value of $\left(\frac{f}{g}\right)\left(x\right)$. Then select correct matching choice from the given choices.

Now let's find  $(fof)(3)$

$\left(\frac{f}{g}\right)\left(x\right)$

$\left(\frac{f}{g}\right)\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}$

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

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

$\left(\frac{f}{g}\right)\left(x\right)=\sqrt{x+1}$

Hence choice A is correct

Answer 2

Answer:

a. (f/g)(x) =  √x+1

Step-by-step explanation:

We have given two function.

f(x)  = √x²-1

g(x)  = √x-1

We have to find the quotient of f(x) and g(x).

(f/g)(x) = ?

The formula to find (f/g)(x) is :

(f/g)(x) = f(x) / g(x)

simplifying f(x) , we have

f(x)  = √(x-1)(x+1)

f(x)  = (√x-1)(√x+1)

Putting values in above formula, we have

(f/g)(x) = (√x-1)(√x+1) / √x-1

(f/g)(x) =  √x+1 which is the answer.