The log function is defined for all numbers greater than 0.
The domain of a function f(x) is all values of x for which f(x) is defined.
For y = log(3) (5x^2 - 125) we should have 5x^2 - 125 > 5 for y to be defined.
5x^2 - 125 > 0
=> x^2 > 125/5
=> x^2 > 25
=> x > 5 and x < -5
The domain of the function is (-inf , -5) U (5 , inf.)
y= log3 ( 5x^2-125)
We need to find the domain.
The domain is all x values such that the function y is defined.
Since the function is a logarithm, then we know that the logarithm should be greater than, zero.
==> (5x^2-125) > 0
We will add 125 to both sides.
==> 5x^2 > 125
==> x^2 > 25
==> l x l > 5
==> x > 5 and x < -5
Then the domain is :
x = ( -inf, -5) U (5, inf)
The domain of f(x) = `log_3 ( 5x^2-125)` has to be determined. The domain of a function f(x) is the set of values in which x lies such that the value of f(x) is real and defined.
The logarithm of 0 or a negative number is not defined.
As a result 5x^2 - 125 > 0
x^2 > 25
=> -5 < x and x > 5
The required domain is `(-oo, -5)U(5, oo)`