Respuesta :
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)
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.
