If f(x) = x² - 25 and g(x) = x - 5, what is the domain of (f/g)(x) and find (f/g)(1)?

Solution:

Given f(x) = x² - 25 and g(x) = x - 5

A function is defined as a relationship between one variable (the independent variable) and another variable (the dependent variable).

(f/g)(x) = f(x)/g(x) = (x² - 25)/ (x - 5)

The domain of a function is the set of all possible inputs for the function.

When the denominator is zero, the function remains undefined. Hence, x cannot take the value 5.

The function (f/g)(x) is defined for all values of x except x = 5

Hence, the domain is all integers except x = 5

⇒ (f/g)(1) = (1)² - 25 / 1 - 5

⇒ (f/g)(1) = 1 - 25 / -4 = -24/-4 = 6

⇒ (f/g)(1) = 6

If f(x) = x² - 25 and g(x) = x - 5, what is the domain of (f/g)(x) and find (f/g)(1)?

Summary:

If f(x) = x² - 25 and g(x) = x - 5, then the domain of (f/g)(x) is all integers except 5 and (f/g)(1) value is 6.