8767 #63

Forum for the GRE subject test in mathematics.
MathCat
Posts: 139
Joined: Thu Oct 23, 2014 12:17 am

8767 #63

Postby MathCat » Thu Oct 23, 2014 12:24 am

Can anyone explain the answer to #63 on 8767?

Let f be a continuous, strictly decreasing, real-valued function such that \int_0^\infty f(x)dx is finite and f(0)=1. In terms of f^{-1} (the inverse function of f), \int_0^\infty f(x)dx is...
(a) less than \int_1^{\infty} f^{-1}(y)dy
(b) greater than \int_0^{1} f^{-1}(y)dy
(c) equal to \int_1^{\infty} f^{-1}(y)dy
(d) equal to \int_0^{1} f^{-1}(y)dy
(e) equal to \int_0^{\infty} f^{-1}(y)dy

The answer is D.

antoniechan
Posts: 1
Joined: Thu Oct 23, 2014 4:12 am

Re: 8767 #63

Postby antoniechan » Thu Oct 23, 2014 4:14 am

just sketch the graph of the function

shade the region of the given integral

rotate your paper and you will see why the answer is D




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