Is a function differentiable at a cusp?

In particular, any differentiable function must be continuous at every point in its domain. The converse does not hold: a continuous function need not be differentiable. For example, a function with a bend, cusp, or vertical tangent may be continuous, but fails to be differentiable at the location of the anomaly.

How do you tell if a function is continuous or discrete?

A discrete function is a function with distinct and separate values. A continuous function, on the other hand, is a function that can take on any number within a certain interval. Discrete functions have scatter plots as graphs and continuous functions have lines or curves as graphs.

How do you show a function in C Infinity?

A function is C1 if its derivative is continuous. A function is C-infinity if derivatives of all order are continuous.

How do you find the inverse of f(x)?

f -1 (x) is the standard notation for the inverse of f (x). The inverse is said to exist if and only there is a function f -1 with ff -1 (x) = f -1 f (x) = x Note that the graph of f -1 will be the reflection of f in the line y = x. This video explains more about the inverse of a function

How do you find the value of Y when x is 4?

Functions. 1 y can be written in terms of x (e.g. y = 3x ). 2 If f (x) = 3x, and y is a function of x (i.e. y = f (x) ), then the value of y when x is 4 is f (4), which is found by replacing x”s by 4″s .

What does the letter F mean in math?

A letter such as f, g or h is often used to stand for a function. The Function which squares a number and adds on a 3, can be written as f (x) = x2+ 5. The same notion may also be used to show how a function affects particular values.

How do you know if a function is one to one?

We say that a function is one-to-one if, for every point y in the range of the function, there is only one value of x such that y = f (x). f (x) = x 2 is not one to one because, for example, there are two values of x such that f (x) = 4 (namely –2 and 2). On a graph, a function is one to one if any horizontal line cuts the graph only once.