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Chapter 5: Q.18 (page 349)

Find the domain of each logarithmic function:

Hx=log2x2-3x+2

Short Answer

Expert verified

The domain of the logarithmic function is2,鈭�

Step by step solution

01

Given expression

Hx=log2x2-3x+2

02

Concept used

By properties of the logarithmic function,

If the function is y=logax, then

Domainofthelogarithmicfunction=Rangeoftheexponentialfunction=0,鈭�, wherex>0

03

Evaluate

The domain of Hconsists of all xfor which

x2-3x+2>0

By factor,

x-2x-1>0

So, role="math" localid="1646457513137" x>2and role="math" localid="1646457519202" x>1

That is, role="math" localid="1646457523294" x>2

Using interval notation,

The domain of His2,鈭�.

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Most popular questions from this chapter

Begin with the graph of y=ex and use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

fx=-ex

The domain of a one-to-one functionf is [0,鈭�), and its range is[5,鈭�). State the domain and the range of f-1.

The domain of a one-to-one functionf is[5,鈭�) , and its range is[-2,鈭�). State the domain and the range off-1 .

A function fhas an inverse function. If the graph of f lies in quadrant I in which quadrant does the graph of f-1 lie?

The domain of a one-to-one functiong is(-鈭�,0) , and its range is[0,鈭�). State the domain and the range ofg-1 .
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