f(x)=ln(x+4), domain, range, graph, and its inverse

TL;DR

The video explains how to find the domain, graph, range, and inverse of the function f(x) = Ln(x) + 4.

Transcript

for this question we are given the function f of X is equal to Ln of X plus 4 and then we have to do these questions I know it has a lot of questions but it's ok because I know you can handle it for the first part is that we are going to find the domain of F this is Ln of X plus 4 Ln is log base e so we are talking about log function so that means ... Read More

Key Insights

• ☺️ The domain of f(x) is given by x > -4.
• ☺️ The graph of the function has a vertical asymptote at x = -4 and approaches positive infinity as x increases.
• ♾️ The range of the function is (-infinity, infinity), indicating that the y-values can be any real number.
• 😀 The inverse of f(x) is given by y = e^x - 4.
• 🧡 The domain of the inverse is the range of the original function.
• 🤪 The graph of the inverse has a horizontal asymptote at y = -4 and goes up towards positive infinity as x increases.
• ♾️ The range of the inverse is (-infinity, infinity), indicating that the y-values can be any real number.

Summary & Key Takeaways

• The video discusses finding the domain of the function f(x) = Ln(x) + 4 by setting the inside of the logarithm greater than 0.

• It explains how to graph the function by selecting various x-values and solving for corresponding y-values.

• The video also covers the range and asymptotes of the function, as well as finding the inverse by switching x and y and isolating y.