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Chapter 5: Q 23. (page 257)

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

f(x)=xx-1andg(x)=-4x

Short Answer

Expert verified

The domain of the composite function of f(x)=xx-1andg(x)=-4xis

localid="1647231939561" (-鈭�,-4)鈭�(-4,0)鈭�(0,鈭�).

Step by step solution

01

Step 1. Given information.

We have given,

f(x)=xx-1andg(x)=-4x

02

Step 2. Concept used.

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

03

Step 3. Explanation.

We have,

f(x)=xx-1andg(x)=-4x

The function g(x) is defined for all real numbers except x = 0.

So domain of the g(x) is the set of all real values of x except 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 of g(x) that value of x for which g(x)=1.

That is,

-4x=1

Solving it for x,

So domain of the composite function is the set of all real numbers except x=-4andx=0.

Domain: (-鈭�,-4)鈭�(-4,0)鈭�(0,鈭�).

04

Step 4. Conclusion.

Hence domain of the composite function of f(x)=xx-1andg(x)=-4xis(-鈭�,-4)鈭�(-4,0)鈭�(0,鈭�).

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