Question

Write the exponential function / (x)=-4.2^(1-x) in the form f(x) = ab^x

Answer 1

Given the equation of the function f(x):

$f(x)=-4\cdot2^{(1-x)}$

We will use the following rules of the exponents:

$\begin{gathered} a^{m+n}=a^m\cdot a^n \\ a^{-m}=\frac{1}{a^m} \\ a^{mn}=(a^m)^n \end{gathered}$

So, we can rewrite f(x) as follows:

$\begin{gathered} f(x)=-4\cdot2^{(1-x)} \\ f(x)=-4\cdot2^1\cdot2^{-x} \\ f(x)=-4\cdot2\cdot(2^{-1})^x \\ \\ f(x)=-8\cdot(\frac{1}{2})^x \end{gathered}$

So, the answer will be option B