Precalculus Functions are based on concept of dependence. For example total surface area of a circle can be determined if we know radius of circle. Thus area of circle is a function of radius and varies with value of radius. Mathematically it can be stated as: If there are two variables 'h' and 'k' such that first variable is dependent on value of independent variable 'k', then relation is said to be a function if and only if we get unique outputs for arbitrary values of 'k'. In that case we would say that 'h' is a function of 'k'.
Thus a relation to denote a function must be one – one or distinct – valued. For example,h = 4k + 5 is a function. We can check this by substituting arbitrary values of 'k' in relation to get corresponding value of dependent variable 'h'. We put values as:
For k = 0, h = 5,
For k = 1, h = 9,
For k = 2, h = 13,
For k = -1, h = 1,
For k = -2, h = -3,
Thus we see that values of 'h' corresponding to random value of variable 'k' are unique and so it represents a function.
We call value of 'k' as domain and those for 'h' as range for various relations or functions.
In pre calculus functions we do not see domain values or range values; only uniqueness of value of range with respect to domain is considered. Let us suppose one more example which is having a restricted domain:
H = 1 / (k – 2),
Here in this function value of 'k' cannot be equals to 2 because corresponding range value comes out to be positive infinity whose value is not defined.
Inverse of a function means to evaluate value of independent variable for which function is defined, in terms of dependent variable. Domain and range for function are evaluated. Inverse of function has domain and range exactly opposite of original domain. Suppose we have a function y = f (x), then inverse of “f (x)” will have domain defined for values of 'y' ...Read More
Set of outputs are known as range in math for as function and set of inputs is known as domain of function. Here we will see how to define range in math. Here we will use some steps to find the range of a function. Steps to be used to calculate the range of given functions are shown below:
Step 1: Put (assume) some values for one variable to calculate the values of other ...Read More