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

Question

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

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Audrey 2 weeks 2021-09-28T04:15:41+00:00 2 Answers 0

Answers ( )

  1. Charlotte
    0
    2021-09-28T04:16:51+00:00

    Answer:

    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)

  2. Charlotte
    0
    2021-09-28T04:17:06+00:00

    Answer:

    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.

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