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If f(x) = 5x + 1 then its inverse function is given by f^-1(x) = ...? Explainnn.
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\[y=f(x)\] \[y = 5x+1\] \[\frac{y-1}{5}= x\] Hence \[f^{-1}(x) = \frac{x-1}{5}\]
x=5y+1 5y=x-1 y=(x-1)/5 f^-1=(x-1)/5
To find \(f^{-1}(x)\) remember that \(f(f^{-1}(x)) = x\) Therefore: \[f(f^{-1}(x)) = 5(f^{-1}(x)) +1\]\[\implies x = 5f^{-1}(x) + 1\]\[\implies x-1 = 5(f^{-1}(x))\]\[\implies f^{-1}(x) = \frac{1}{5}(x-1)\]
Or at least that's how I remember
that makes absolutely no sence at all! I really don't understand f(x) at all. & when you add a ^-1 in there, it throws me off twice as much.
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