If $f(x)=a x+b$ and $f^{-1}(x)=b x+a$ for $a, b \in \mathbb{R}$, then $a+b=$

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Professor PC Thomas Classes · Answer

Composition $f(f^{-1}(x))=x$ mandates $ab=1$ and $a^2+b=0$. Isolating valid reals requires $a=-1$ and $b=-1$.