If 2 functions g(x) & f(x) are defined so that (f ο g) (x) = x and (g ο f) (x) = x we say
that g(x) & f(x) are inverse functions of each other.
Functions f(x) & g(x) are inverses of each other in case the operations of g(x) reverse all the operations of f(x) in the reverse order & the operations of f(x) reverse all the operations of g(x) in the reverse order
The Best Example: Determine the inverse log function of f(x) = log(x + 5).
A function is called increasing when it increases as the variable increases & decreases as the variable decreases. A function is called decreasing when it decreases as the variable increases & increases as the variable decreases.
The graph of a function specifies plainly whether it is increasing or decreasing.
The derivative of a function can be used to determine whether the function is decreasing or increasing on any intervals in its domain. Incase f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) <>decreasing on I. Because the derivative is 0 or does not exist only at critical points of the function, it must be negative or positive at all other points where the function exists.
Theorem on Decreasing or Increasing of Functions:
Let letter “f” be continuous on [a, b] & differentiable on the open interval (a, b).
(a)“f” is decreasing on [a, b] if f '(x) <>ε(a, b)
(b) “f” is increasing on [a, b] if f '(x) > 0 for each x ε(a, b)
Theorem on Decreasing or Increasing of Functions can be proved by using Mean Value Theorem.
Theorem on Decreasing or Increasing of Functions can be used in various problems to check whether a function is increasing or decreasing.
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Definite integral calculator is same as the integral calculus calculator but it is mostly for finding the integral which is covered by a specific intervals. That is definite integral calculator has upper limit value & lower limit value.
For this definite integral calculator 1st the given expression should be integrated as integral calculator & then the limits should be applied. The final output can be derived by substituting the lower limit - upper limit
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A number line is a line of real numbers can be arranged, according to their value. Each point on a number line corresponds to a real number& each real number has a distinctive (unique) point which corresponds to it. The best example, the number 1.5 (1 1/2) corresponds with the point on a number line which is halfway between 1 & 2.
The points on a number line are said to be as coordinates. The point zero is called the origin. & the numbers to the left side of the origin are negative numbers & the numbers to the right side of the origin are positive numbers. The counting numbers are starting from 1.These numbers are also said to be as natural numbers. Natural numbers are numbers that was a base of the number system. The number line to 20 will help student to understand the basic things in number theory. This type of number line will includes of numbers from 1 to 20.
That is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 and 20.
So totally 20 numbers...
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Learning how to divide decimals is essential to learn math. It can get tricky, especially when student dealing with long decimals with many places. Here there is a step-by-step guide to help student get through this procedure.
Moving Decimals
The 1st step in decimal division is to check the divisor for decimal places. The divisor is the number that is outside of the division symbol or the 2nd number in the equation. If the divisor has a decimal, student need to move the decimal over as many places as it takes to make it a whole number. Consider the following example:
4.2512 / .125
In order to make .125 into a whole number, student must move the decimal place over 3 sots to the right to get 125. When student do this, student must also move the decimal in the dividend the number under the division sign or the 1st number in the equation, the same numbers of spaces. In this example, student would move it over 3 spaces to get 4251.2. Now the equation looks like this:
4251.2 / 125
Doing the Math the next step is to divide the numbers as student normally would until there is no remainder. Student should get the number 340096 resting on top of the roof of the division symbol. The final step is the most important part. Student need to take the decimal in the dividend & move it directly above to the result. Now solution should read 34.0096.
Learning decimals takes some time & to practice, so make sure to provide Student with many examples. Students can always double-check their solution by multiplying the answer by the divisor to see if it equals the dividend. If it doesn't, student should know they made a mistake.
In our next blog we shall learn about how to divide numbers I hope the above explanation was useful.Keep reading and leave your comments.
Free Calculus Help website is dedicated to providing resources to students & help on the mathematical branch of calculus. Calculus help is free & includes calculus tutorial, calculus problems, & many best examples of how to learn calculus. Learning calculus can be difficult at 1st especially integral calculus but after understanding some basics rules of calculus, calculus problems should become much easier. Free Calculus Help website provides calculus help in many fields of mathematical calculus.
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Most of the calculus help on this Free Calculus Help website is pre calculus, including more advanced calculus, more AP calculus & more Pre Calculus materials. Learning calculus can be challenging at 1st, but don't give up. There are much calculus help out there and many resources of calculus help are free calculus help such as this Free Calculus Help website. Learn calculus with our online calculus tutor & online calculus tutorial. Tutors will help students to solve integration problems & differentiation problems. Share your calculus problems that you cannot solve so that other learners of calculus may help you. The chances are if you find some calculus problems difficult, other learners of calculus will find the same calculus problems difficult too. Let tutors know of the calculus problems you cannot solve and let the calculus community help you solve calculus problems.
Integral calculus is 1 of the more difficult areas of calculus. The more advanced calculus you are studying, the more tricky the integral calculus problems you will come across. However, it does get better! Calculus problems, especially integral calculus problems only get difficult up to a certain level. After that level, integral calculus problems do not get any more difficult. Once you have leaned all the rules of integral calculus and the tricks to solving integral calculus problems, other problems are just duplicates of the same methods of solving those integral calculus problems. So, keep learning calculus!
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