Question

Find (f/g)(x)

A
B
C
D

Answer 1

Choice a is correct answer.

Explanation:

We have given two function.

f(x) = √x²-1

g(x) = √x-1

We have to find the quotient of given functions.

(f/g)(x) = ?

The formula to find quotient of two function:

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

Putting given values in above formula, we have

(f/g)(x) = √x²-1 / √x-1

(f/g)(x) = √(x-1)(x+1) / √x-1

(f/g)(x) = √x-1√x+1 / √x-1

(f/g)(x) = √x+1 which is the answer.

Answer 2

Option (a) is correct.

`(f(x))/(g(x))=√(x+1)`

Explanation:

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

We have to find the value of
`((f)/(g))(x)`

Consider
`((f)/(g))(x)`

It is same as
`((f)/(g))(x)=(f(x))/(g(x))`

Substitute the value of f(x) and g(x) , we have,

`(f(x))/(g(x))=(√(x^2-1))/(√(x-1))`

Combining same powers ,
`\quad (√(x))/(√(y))=\sqrt{(x)/(y)}` , We have,

`=\sqrt{(x^2-1)/(x-1)}`

Factorize numerator as ,
`x^2-1:\quad \left(x+1\right)\left(x-1\right)`

We have ,
`=(\left(x+1\right)\left(x-1\right))/(x-1)`

Cancel out (x-1) , we get, (x + 1)

`(f(x))/(g(x))=√(x+1)`

Thus, Option (a) is correct.