Question

# f(x) = cos(x) defined on f : [a,b] → [-1,1] has its inverse then which of the following is correct?

A
a=π;b=π
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B
a=0;b=π
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C
a=0;b=2π
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D
None of these
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Solution

## The correct option is B a=0;b=πWell, we know that for a function to have an inverse, the function should be one- one onto. We can see the co- domain given in the question is same as the range of cos(x). So now we only have to see that interval in which cos(x) is one - one. It is very simple, just draw horizontal lines, if any line cuts the curve at more than one point then it’s a many one function whereas if no line cuts more than once then it’s a one - one function. Let’s check the options given one by one. a=−π;b=π We can see that a horizontal line shown is cutting the curve at two points. So this options can’t be correct. b. a=0; b=π We can see that we cannot find any line which would cut the graph more than once in the interval given. Actually the function is a strictly decreasing function in the interval. Thus we can define the inverse for the function in this interval. And thus it is the answer. C.a=0;b=2π In this interval also we can see that there are many lines we can get which will cut the graph at more than one points.

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