MathDB
Three functions

Source: 1988 National High School Mathematics League, Exam One, Problem 1

February 25, 2020
function

Problem Statement

We have three functions. The first one is y=ϕ(x)y=\phi(x). The second one is the inverse function of the first one. The figure of the third funcion is symmetrical to the second one about line x+y=0x+y=0. Then, the third function is (A)y=−ϕ(x)(B)y=−ϕ(−x)(C)y=−ϕ−1(x)(D)y=−ϕ−1(x)\text{(A)}y=-\phi(x)\qquad\text{(B)}y=-\phi(-x)\qquad\text{(C)}y=-\phi^{-1}(x)\qquad\text{(D)}y=-\phi^{-1}(x)
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