Inverse functions, domain and range??

Posted on Mar 23, 2008 under domain news and reports | 5 Comments

1.) Let h(x) = ln(x+7) – 1

a.) find the inverse of f
b.) determine the domain and range of f and the inverse of f

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5 Responses to “Inverse functions, domain and range??”

  1. Rackbrane Says:
    March 23rd, 2008 at 7:15 am

    (a)
    y = ln(x + 7) + 1
    y – 1 = ln(x + 7)
    e^(y – 1) = x + 7
    x = e^(y – 1) – 7

    The inverse function is:
    f(x) = e^(x – 1) – 7.

    (b)
    ln(x) is defined for all x > 0. The domain is (0, infty), and the range is (- infty, infty).

    ln(x + 7) – 1 is defined when:
    x + 7 > 0
    x > – 7
    The domain is therefore (- 7, infty), and the range is (- infty, infty).

    e^x has domain (- infty, infty) and range (0, infty).
    e^(x – 1) has domain (- infty, infty) and range (0, infty).
    e^(x – 1) – 7 has domain (- infty, infty) and range (- 7, infty).

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