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A math problem in senior high school: How to calculate the period of f(x+a)=f(x+b) and f(a+x)=f(b-x)? thank you
If f(x+a)=f(x+b), the function changes periodically: the minimum positive period T= internal large variable minus internal small variable.

f(x+ 1)= f(x-2)= = & gt; T=3

f(x+ 1)=-f(x-2),= =》T/2 = 3 = = & gt; T=6 (internal subtraction is constant)

f(x+ 1)= f(2-x)= & gt; The symmetry axis is: x=(x+ 1+2-x)/2=3/2 (the internal addition is unchanged).

F (x+ 1) =-f (2-x) The abscissa of the symmetry point is x=3/2, and the ordinate is equal to 0.