Question

Let f(x) = px^2 and g(x) = log(x^2) , then gof(x) is:

a) ( x^2 )
b) ( x^4 )
c) ( x )
d) ( 1 )
e) NOTA (None of the Above)

Answer 1

When composing the functions f(x) = px^2 and g(x) = log(x^2), the result is g(f(x)) = 4log(x), which is not among the given answer choices. Hence, the correct answer is e) NOTA (None of the Above).

Step-by-step explanation:

The question asks for the composition of two functions, specifically g(f(x)). Here, f(x) = px^2 and g(x) = log(x^2). To find g(f(x)), you substitute f(x) into g(x).

Firstly, we have:

• f(x) = px^2

Now, we apply g to f(x) to get:

• g(f(x)) = log((px^2)^2)

We can simplify this using the logarithmic property that states: The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. As such:

• g(f(x)) = log(p^2x^4)
• g(f(x)) = 2log(p) + 4log(x)

However, since we're only interested in the x variable and p is a constant, the final term that includes x is 4log(x). This expression is not one of the offered answers, therefore the correct answer is e) NOTA (None of the Above).