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10 cards from this deck
It must be one-to-one (1-to-1).
f(x)=x2f(x) = x^2f(x)=x2, x∈Rx \in \mathbb{R}x∈R has no inverse.
Restrict to a one-to-one portion of the function.
f−1(x)=xf^{-1}(x) = \sqrt{x}f−1(x)=x.
Swap xxx and yyy, then rearrange to find yyy.
f−1(x)=ln(x)f^{-1}(x) = \ln(x)f−1(x)=ln(x).
Range is f(x)>0f(x) > 0f(x)>0.
f−1(x)=(x−3)/2f^{-1}(x) = (x - 3)/2f−1(x)=(x−3)/2.
The xxx and yyy coordinates are swapped to find its inverse.
They intersect at (k,k)(k, k)(k,k) where f(k)=kf(k) = kf(k)=k.
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