Determine all linear functions f(x) = ax + b such that if g(

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Determine all linear functions f(x) = ax + b such that if g(x) = f^−1(x) for all
values of x,then f(x) − g(x) = 44 for all values of x.

找一个线性方程,这个方程和自己的inverse方程的差总为44
Y=x+22;y=x-22
再问：能告诉我怎么做的嘛？
再答： f(x) = ax + b x=[f(x)- b]/a 把x,f(x)换一下可得 g(x) = f^−1(x)=[x- b]/a f(x) − g(x) =ax + b - [x- b]/a=(a-1/a)x+b+b/a=44恒成立，所以a-1/a=0且b+b/a=44，所以a=1,b=22
再问：为什么a-1/a=0?对不起我比较笨- -
再答：因为对于任意的x，式子f(x) − g(x) = 44都要成立啊。也就是说式子与x无关。所以x前面的系数应该是0。。这样说懂了么？

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