Gaokao Math Problem

 




(1) If the graph of function y = f(x) and y = log3x (x>0) are symmetrical of line y=x, then f(x) = ________.

(2)
If f(x) is an odd function, then a = ________.

Solution:
(1) If f(x) and y = log3x are symmetrical of line y=x, then f(x) is the inverse of log3x.
We find the inverse of log3x:
x = log3y
y = 3x
The correct answer is f(x) = 3x

(2) If f(x) is an odd function, f(x) = -f(-x).











a = -1