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Math

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determine if the given function is one-to-one. if it is, find the inverse.
f(x) = 8x - 4

A) f-1(x) = x+4 / 8
B) f-1(x) = x-4 / 8
C) Not one-to-one
D) f-1(x) = x/8 + 4

  • Math -

    All functions that are strictly increasing or decreasing in its domain are one-to-one.
    Since the given function has a constant positive slope, it is strictly increasing over ℝ, so it is one-to-one.

    The inverse can be found as follows:
    1. interchange x and y to get
    from f(x) = y = 8x - 4
    to
    x=8y-4
    2. Solve for y in terms of x:
    8y=x+4
    y=(x+4)/8

    Now there is sufficient information to find the correct answer.

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