Question

1. consider the curve $y = 2(4^x)$. what is the domain of the function? a all real x b $x \geq 0$ c $x \geq 4$ d $x < 2$

Explanation:

Step1: Recall the definition of domain

The domain of a function is the set of all possible input values (x - values) for which the function is defined.

Step2: Analyze the exponential function \(y = 2(4^{x})\)

For an exponential function of the form \(y = a(b^{x})\) where \(a\) and \(b\) are constants (\(b>0,b
eq1\)), there are no restrictions on the value of \(x\). The function \(y = 2(4^{x})\) is an exponential function. Since \(4>0\) and \(4
eq1\), for any real - number \(x\), the expression \(4^{x}=\text{e}^{x\ln4}\) is well - defined.

Answer:

A. all real \(x\)