Calculus is deemed as one of the toughest branches of Math and it is also felt that those who are gifted with a special brain for Math have the courage to choose Calculus courses. Those who choose it also find it brain storming many a time for the problems it shows forth and the mental exercises it demands. Many students find it excruciating, if they do not hold good fundamental knowledge in Algebra and Trigonometry. Still, taking high school Calculus and acing the subject is the gateway for college Calculus and many advanced Math courses.
What you need to know about Calculus?
To define in very simple terms, Calculus is the study of change.
It has two main branches, Differential Calculus and Integral Calculus.
To excel in Calculus, you need the skills of Algebra and Trigonometry.
High school Calculus topics are Limits, Derivatives, Integrals and Applications of Derivatives etc. Students find these topics and other ones in Calculus tough, if they do not follow their classes regularly or are not motivated to do Calculus.
Let us see one question on Inverse Functions with solution now
Prove that the inverse of an invertible odd function is also an odd function.
- Start with the property of f and its inverse f -1f ( f -1(x)) = x
- Change the right side x of the above equation to – (-x) and writef ( f -1(x)) = – ( – x)
- Again change – x in the above equation to f ( f -1( – x)) and writef ( f -1(x)) = – f ( f -1( – x))
- Since f is odd, the right side in the above equation may be written as follows- f ( f -1( – x)) = f( – f -1( – x) )
- Hencef ( f -1(x)) = f( – f -1( – x) )
- Which givesf -1(x) = – f -1( – x)
- And proves that f -1 is also odd.
When you come across such questions and get stuck up in the middle, you feel like giving up the subject and do not know the way to move on. Online High School Calculus Tutors are your best bet on such occasions and they help you with explanations on the interactive white board step by step and help you wade through the problem.
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