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9 May, 09:09

State the inner and outer function of f (x) = arctan (e^ (x))

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Answers (2)
  1. 9 May, 10:50
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    The inner function is v (x) = e^x

    and the outer function is f (x) = arctan (e^x)

    Step-by-step explanation:

    Given f (x) = arctan (e^x)

    Let v = e^x, and f (x) = y

    Then y = arctan (v)

    This implies that y is a function of u, and u is a function of x.

    Something like y = f (v) and v = v (x)

    y = f (v (x))

    This defines a composite function.

    Here, v is the inner function, and arctan (u) is the outer function.

    Since v = e^x, we say e^x is the inner function, and arctan (e^x) is the outer function.
  2. 9 May, 12:21
    0
    So the inner function is g (x) = arctan (x) and the outer function is h (x) = e^ (x)

    Step-by-step explanation:

    Suppose we have a function in the following format:

    f (x) = g (h (x))

    The inner function is h (x) and the outer function is g (x).

    In this question:

    f (x) = arctan (e^ (x))

    From the notation above

    h (x) = e^ (x)

    g (x) = arctan (x)

    Then

    f (x) = g (h (x)) = g (e^ (x)) = arctan (e^ (x))

    So the inner function is g (x) = arctan (x) and the outer function is h (x) = e^ (x)
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