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Sir in this question how is the inverse fn derived. Pls explain in details.

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Asked by rsudipto 15th December 2018, 8:55 AM
Answered by Expert
Answer:
Figure.(1) shows the plot of the function f(x) = x + sin(x) along with the plot of function f(x) = x .
Obviously the function f(x) = x+sin(x) is overlap of sin(x) on the line of f(x) =x .
 
The inverse function of x+sin(x) is defined as  f(x) = x-sin(x). It is just definition. It is not calculated using any guidelines.
Inverse function x-sin(x) is plotted in figure. It can be seen from figure.(2) and figure. (3) the function x+sin(x) and
its inverse are mutual reflection of other with respect to the line f(x) = x. It appears mirror is placed along the line f(x) = x
and both the fuctions are getting reflected. That is why the function ' x-sin(x) ' is called the inverse of ' x+sin(x) ' and vice versa.
 
Area enclosed between the two functions (Shaded area in figure 3) = begin mathsize 12px style integral subscript 0 superscript 2 straight pi end superscript space left square bracket space left parenthesis x plus sin left parenthesis x right parenthesis right square bracket space minus space left square bracket x minus sin left parenthesis x right parenthesis right square bracket space equals space 2 integral subscript 0 superscript 2 straight pi end superscript sin left parenthesis x right parenthesis space equals space 8 space s q. u n i t s end style
Answered by Expert 16th December 2018, 4:10 PM
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