Question

Help me what is the answer?!

Answer 1

a. (f/g)(x) = √x+1

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.

Answer 2

Hence choice A is correct

Explanation:

Given equations are
`f(x)=√(x^2-1)` and
`g(x)=√(x-1)`

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

Now let's find
`(fof)(3)`

`\left((f)/(g)\right)\left(x\right)`

`\left((f)/(g)\right)\left(x\right)=(f\left(x\right))/(g\left(x\right))`

`\left((f)/(g)\right)\left(x\right)=(√(x^2-1))/(√(x-1))`

`\left((f)/(g)\right)\left(x\right)=(√(\left(x+1\right)\left(x-1\right)))/(√(x-1))`

`\left((f)/(g)\right)\left(x\right)=√(x+1)`

Hence choice A is correct