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Find the inverses of each of the functions below algebraically.


a.p(r)=2r2+2r−1

b.3y+5x=18

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  1. p = 2r^2+2r-1
    swap variables
    r = 2p^2+2p-1
    2p^2+2p-(1+r) = 0
    p = [-2 +/- sqrt(4+8(1+r))]/4
    = [-2 +/- sqrt(8r+12)]/4
    = [-1 +/- sqrt(2r+3)]/2

    So, what's with the 2 values? The original function fails the horizontal-line test, so it has no single inverse. However, if the domain is restricted to a single branch of the parabola (the vertex is at r = -1/2) then the inverse is one of the two values calculated.

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