i know the domain is (-3 , infinity)
y = ln(x+3)
i thought it was [-4, infinity) but i checked on a calculator and it goes passed -4. And i cannot use a calculator
Printable View
i know the domain is (-3 , infinity)
y = ln(x+3)
i thought it was [-4, infinity) but i checked on a calculator and it goes passed -4. And i cannot use a calculator
The range of a function is the set of numbers the function can achieve. The natural log has a range $\displaystyle (-\infty,\infty)$. However, its domain is $\displaystyle (-3,\infty)$. The domain is the set of numbers for which the function is defined. Natural log can take numbers from $\displaystyle (0,\infty)$. So we just need to check when $\displaystyle x+3 > 0$.
What is the range of $\displaystyle \ln x$ ?
An easy way to remember the range of the natural log is to recall that $\displaystyle ln|a| = x \implies $ $\displaystyle a = e^x $.
its (-inf, inf) so all real numbers?
Yep!
It may be helpful to remember from now on that the domain of the basic f(x) = ln x is (0, ∞) and that the range is (-∞, ∞). In my textbook it's considered one of the twelve basic functions.
