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Describe one advantage of using $f(x)$ rather than $y$ in a function's equation.How is the domain of a function determined?...

Question

Describe one advantage of using $f(x)$ rather than $y$ in a function's equation.How is the domain of a function determined?

Describe one advantage of using $f(x)$ rather than $y$ in a function's equation. How is the domain of a function determined?



Answers

Explain why the domain of $f(x)=\sqrt[3]{x}$ is different from the domain of $f(x)=\sqrt{x}$

Okay, the domain of a function essentially deep numbers or coordinates for which the function is valid. So there's two things you have to do to find the domain. The 1st 1 is do not have any values that result in division by zero. So in other words, X divided by zero can't happen because X divided by zero is the same thing is undefined. So in other words, you can't have any values that are undefined. Is that it? Then the function value is not true for these values. So nothing you could never have zero on the bottom because you can't divide by zero. Next, you can't have any undefined output. So no undefined outputs. And this goes off of the first part because if you can't divide by zero, then you can't have undefined outfit outputs.

Okay, so these two functions have a different domain because where they can be defined is different. So in this case, in vehicles the cube root of X every route every value of X produces a rail route. So that domain here interval notation is from negative infinity to infinity. Here, though, the square root of X does not allow negative numbers. For example, the square moves of negative one. If X equals negative one, we're not.

Says If you were given, why was f of X? Yeah, As a function you just told it some function of X. How do you find ah Wai Prime? We're at the front of X. Hey, So how do we find this? So all we would do is take the derivative and the derivative The limit definition. Truman is this. So use this formula. Hey, the limit is age approaches. Zero f x plus h minus that fax over age. That's what we would do and we would apply that formula. I'm sorry, and we would get her answer.

Mia Bella, Number 100. We have to discuss advantage of function. Rotation, so advantages we can directly Oh, sorry. This is another advantage. Advantage will be It helps us toe understand the nature off the function. And but to get a new idea I did that. Yeah. Which the is dependent. Wisdom is the dependent term. Or which variable we believe is the independent variable. Thank you. And okay, which is the independent variable on the dependent variable. For example, if you take an example of function affects equal to excuse minus two. So since this is effects so this must be the dependent, variable, dependent variable which will depend on the values effects, So access the independent variable. Thank you.


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