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Chapter 5: Q 46. (page 298)

Find the domain of the function :h(x)=log3(xx-1)

Short Answer

Expert verified

The domain of the given function is :(-鈭�,0)鈭�(1,鈭�)

Step by step solution

01

Step 1. Given information

Given expression is h(x)=log3(xx-1)

Domain : The range of xis known as domain of definition.

02

Step 2. Find domain

The domain of definition of the function is the range of the values where xx-1>0.

In this range the function will produce finite values ; xand localid="1651761337072" (x-1)both will be either positive or negative.

Now, (x-1)will be positive in the range localid="1651761514492" (1,鈭�)and xwill be positive in the range (0,鈭�).

Again, (x-1)will be negative in the range (-鈭�,1)and xwill be negative in the range (-鈭�,0)

Thus, the domain of the given function is(-鈭�,0)鈭�(1,鈭�)

03

Step 3. Check

log(0)is undefined.

Hence, the function is discontinued from 0鈮�x鈮�1

Hence, the domain of the function islocalid="1651761601326" (-鈭�,0)鈭�(1,鈭�)

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