The expression e^x / e^(4+x) can be written as e^f(x), where f(x) is a function of x, find f(x)?
e^x / e^(4+x)
= e^(x-(4+x))
= e^-4
so f(x) = -4
Did I misunderstand the question??
To find f(x) for the expression e^x / e^(4+x), we can use the properties of exponents and the rules of division.
First, let's simplify the expression by dividing the numerator and denominator with the same base, which is e:
e^x / e^(4+x) = e^(x - (4+x))
Next, we can combine the exponents within the parentheses:
e^(x - (4+x)) = e^(-4)
Therefore, we can write e^x / e^(4+x) as e^(-4), and f(x) would be -4.
To find f(x) such that e^x / e^(4+x) can be written as e^f(x), we'll need to simplify the given expression.
Let's start by using the property of exponents that states a^m / a^n is equal to a^(m-n).
In this case, we have e^x / e^(4+x), which can be written as e^x / (e^4 * e^x). Applying the exponent property, we get e^(x - (4 + x)).
Simplifying further, we have e^(x - 4 - x), which gives us e^(-4).
Therefore, f(x) = -4.
So, the expression e^x / e^(4+x) can be written as e^(-4).