Question

1. g(x) = 4x

Explanation:

Since the problem statement for \( g(x) = 4x \) is incomplete (e.g., we don't know what is being asked about this function, like finding its derivative, integral, inverse, evaluating at a point, etc.), we can't provide a solution yet. If you want to find the derivative, for example:

Step1: Recall the power rule for differentiation

The power rule states that if \( f(x) = ax^n \), then \( f'(x) = anx^{n - 1} \). For \( g(x)=4x \), we can rewrite \( 4x \) as \( 4x^1 \). Here, \( a = 4 \) and \( n = 1 \).

Step2: Apply the power rule

Using the power rule, \( g'(x)=4\times1\times x^{1 - 1} \). Simplifying the exponent, \( x^{0}=1 \) (since any non - zero number to the power of 0 is 1), so \( g'(x)=4\times1\times1 = 4 \).

If this is not the operation you want, please clarify the question (e.g., find the inverse function, evaluate \( g(5) \), find the integral, etc.).

Answer:

Step1: Recall the power rule for differentiation

The power rule states that if \( f(x) = ax^n \), then \( f'(x) = anx^{n - 1} \). For \( g(x)=4x \), we can rewrite \( 4x \) as \( 4x^1 \). Here, \( a = 4 \) and \( n = 1 \).

Step2: Apply the power rule

Using the power rule, \( g'(x)=4\times1\times x^{1 - 1} \). Simplifying the exponent, \( x^{0}=1 \) (since any non - zero number to the power of 0 is 1), so \( g'(x)=4\times1\times1 = 4 \).

If this is not the operation you want, please clarify the question (e.g., find the inverse function, evaluate \( g(5) \), find the integral, etc.).