Find the Domain and Range f(x) = log base 4 of 3-2x

Problem

ƒ(x)=(log_4)(3−2*x)

Solution

1. Identify the condition for the domain of a logarithmic function, which requires the argument to be strictly greater than zero.

3−2*x>0

2. Solve the inequality for x by subtracting 3 from both sides.

−2*x>−3

3. Divide by −2 and reverse the inequality sign to find the domain.

x<3/2

4. Determine the range by observing that the output of a logarithmic function (log_b)(u) spans all real numbers as u approaches 0 from the right and as u approaches infinity.

Range=(−∞,∞)

Final Answer

Domain: *(−∞,3/2), Range: *(−∞,∞)

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