Question

If f(x) = x2 – 25 and g(x) = x – 5, what is the domain of (f/g)(x)

Answer 1

Choice A is correct answer.

Explanation:

We have given two functions.

f(x) = x² – 25 and g(x) = x – 5

We have to find (f/g)(x).

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

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

Putting given values in above formula, we have

(f/g)(x) = x²-25 / x-5

(f/g)(x) = (x-5)(x+5) / x-5

(f/g)(x) = x+5

Now, domain of above function is all real values of x.

Answer 2

The domain is all real values except x = 5

Explanation:

∵ f(x) =
`x^(2)-25`

∵ g(x) = x - 5

∵
`(f(x))/(g(x))=(x^(2)-25 )/(x-5)`

The domain of it is all the values of x make
`(f(x))/(g(x))` is defined

∴ The denominator can not be zero

∵ x - 5 = 0⇒ means x = 5

∴ We can't use 5 as a value for x

∴ The domain of
`(f(x))/(g(x))` is all the real number except x = 5