## 8767 #63

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

### 8767 #63

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 $$\int_0^{\infty} f^{-1}(y)dy$$