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Chapter 5: Q 21. (page 256)

Find the domain of the composite function (f鈭�g).

f(x)=3x-1andg(x)=2x

Short Answer

Expert verified

Domain of the composite function of f(x)=3x-1andg(x)=2xis(-鈭�,0)鈭�(0,2)鈭�(2,鈭�).

Step by step solution

01

Step 1. Given information.

We have given functions are,

f(x)=3x-1andg(x)=2x

02

Step 2. Concept used.

Domain is the set of all input values where function is real and well defined.

03

Step 3. Explanation.

We have,

f(x)=3x-1andg(x)=2x

Domain of g(x) is the set of all real numbers except x = 0.

Since, the function g(x) is undefined at x = 0.

Similarly domain of the function f(x) is the set of all real numbers except

x = 1.

So we need to exclude from the domain from the g(x) that value of x for which g(x) = 1.

2x=1

Solving it for x we will get,

x=2

So the domain of the f鈭�gis the set of all real numbers except x = 0 and x = 2.

Domain:localid="1647224954786" (-鈭�,0)鈭�(0,2)鈭�(2,鈭�)

04

Step 4. Conclusion.

Hence, domain of composition of the functions f(x)=3x-1andg(x)=2xis(-鈭�,0)鈭�(0,2)鈭�(2,鈭�).

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Most popular questions from this chapter

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.

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and verify your results using a graphing utility.

The graphs ofy=a-x and y=1axare identical. Why?

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