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Chapter 5: Q 24. (page 257)

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

f(x)=xx+3andg(x)=2x

Short Answer

Expert verified

The domain of composite function off(x)=xx+3andg(x)=2xis(-鈭�,-23)鈭�(-23,0)鈭�(0,鈭�).

Step by step solution

01

Step 1. Given information.

We have given,

f(x)=xx+3andg(x)=2x

02

Step 2. Concept used.

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

03

Step 3. Explanation.

We have,

f(x)=xx+3andg(x)=2x

Function g(x) is defined everywhere except x = 0.

So domain of the function is set of all real numbers except x = 0.

Similarly domain of the f(x) is the set of all real values except x = -3.

So we need to exclude from the domain of g(x) that value of x for which g(x)=-3.

2x=-3

Solving it for x,

x=-23

SO domain of the composite function is set of all real numbers except

x = 0 and x=-23.

Domain:(-鈭�,-23)鈭�(-23,0)鈭�(0,鈭�)

04

Step 4. Conclusion.

Hence, domain of the composite function of f(x)=xx+3andg(x)=2xis(-鈭�,-23)鈭�(-23,0)鈭�(0,鈭�).

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