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)=(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((1)/(2))^x \end{gathered}`

So, the answer will be option B