Question

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

Answer 1

Answer:

The domain is all real values except x  = 5

Step-by-step explanation:

∵ f(x) = $x^{2}-25$

∵ g(x) = x - 5

∵ $\frac{f(x)}{g(x)}=\frac{x^{2}-25 }{x-5}$

The domain of it is all the values of x make $\frac{f(x)}{g(x)}$ 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 $\frac{f(x)}{g(x)}$ is all the real number except x = 5

Answer 2

Answer:

Choice A is correct answer.

Step-by-step 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.