题目

已知函数y=f(x),有下列关系式确定:xy

提问时间：2021-12-17

答案

1、4x²-9y²=36--->y²=(4/9)(x²-9)
--->y = f(x) = (2/3)√(x²-9) .x＜-3
=-(2/3)√(x²-9) .x＞3
2、交换x、y--->4y²-9x²=36
---> y²=(9/4)(x²+4)
---> y = f^-1(x) = (3/2)√(x²+4) .x＜0
=-(3/2)√(x²+4) .x＞0
3、f(4) = -(2/3)√(16-9) = -2√7/3
f(-9) = (2/3)√(81-9) = 4√2
f[f(-9)] = -(2/3)√(32-9) = -2√23/3