The term convex function is used in mathematics. It is used to define an interval where the line segment between two points is above the graph, this can both be downward or upward.
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Wherever a function is differentiable, it must also be continuous. The opposite is not true, however. For example, the absolute value function, f(x) =|x|, is not differentiable at x=0 even though it is continuous everywhere.
n. 1. A form or part that is folded or coiled. 2. One of the convex folds of the surface of the brain.
The range of the arcsinx function is restricted because it is the inverse of a function that is not one-to-one, a characteristic usually required for a function to have an inverse. The reason for this exception in the case of the trigonometric functions is that if you take only a piece of the function, one that repeats through the period and is able to represent the function, then an inverse is obtainable. Only a section that is one-to-one is taken and then inverted. Because of this restriction, the range of the function is limited.
If y is an exponential function of x then x is a logarithmic function of y - so to change from an exponential function to a logarithmic function, change the subject of the function from one variable to the other.