caluclus

Find the inverse function f^-1 of the function f. What is the domain of f^-1? What is its range?

f(x) = 5 tan (10x-2)

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  1. switch variables and solve for y:
    x = 5tan(10y-2)
    x/5 = tan(10y-2)
    10y-2 = arctan(x/5)
    y = (arctan(x/5)+2)/10

    In order for tan(z) to have an inverse, -π/2 < z < π/2
    So, we need to restrict f(x) so its domain is
    -π/2 < 10x-2 < π/2
    2-π/2 < 10x < 2+π/2
    (2-π/2)/10 < x < (2+π/2)/10

    Now you can see what the domain and range of the f^-1 are.

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    oobleck

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