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## What are the domain and range of f(x) = 2(3x)?

Option A. Domain = (-Infinity, Infinity); Range (0, Infinity)

Solution:

f(x)=2^(3x)

a) This is an exponential function, and we don’t have restrictions for the independent variable “x” in the exponent, then the Domain of f(x) is all the real numbers:

Domain f(x) = ( – Infinity, Infinity)

b) To find the range we can find the inverse function f^(-1) (x). The domain of the inverse function is the range of the original function f(x):

y=f(x)

y=2^(3x)

Isolating x: Applying log both sides of the equation:

log y = log 2^(3x)

Applying property of logarithm: log a^b = b log a; with a=2 and b=3x

log y = 3x log 2

Dividing both sides by 3 log 2:

log y / (3 log 2)=3x log 2 / (3 log 2)

log y / (3 log 2)=x

x=log y / (3 log 2)

Changing x by f^(-1) (x) and y by x:

f^(-1) (x) = log x / (3 log 2)

This is a logaritmic function and the argument of the logarithm must be greater than zero, then the Domain of the inverse function is:

x>0→Domain f^(-1) (x) = (0, Infinity)

The domain of the inverse is the range of the original function:

Range f(x) = Domain f^(-1) (x)

Range f(x) = (0, Infinity)

Domain f(x) = ( – Infinity, Infinity)

Range f(x) = ( 0, Infinity)

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Find the Domain and Range f(x)=(3x-1)/(x+2) | Mathway – Subscribe for new videos: www.youtube.com/channel/UCIWCSw8jNs9SPetsVPo1WQQShare this video: https://youtu.be/qpnJcI6XuQMThe problem: Make a function table fo…[math]2(3x) = 6x[/math] For the domain, ask what number can I plug in so that the function is undefined (e.g. division by 0)? In this case, there is nothing you can plug in to make it undefined so the domain is all real numbers: [math](-\infty,\in…What is the range of the function f(x) = 3x − 12 for the domain {-2, 2}? A. {3, 12} B. {-6, -18} C. {-18, -6} D. {6, 18} E. {12, 3} – 4468568

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