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

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03-11-2022
Mathematics

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

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LileeannX63841 LileeannX63841 · Answer 1 · 2022-11-03T14:21:46-04:00

Given the equation of the function f(x):

[tex]f(x)=-4\cdot2^{(1-x)}[/tex]

We will use the following rules of the exponents:

[tex]\begin{gathered} a^{m+n}=a^m\cdot a^n \\ a^{-m}=\frac{1}{a^m} \\ a^{mn}=(a^m)^n \end{gathered}[/tex]

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

[tex]\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}[/tex]

So, the answer will be option B

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