Find the composite functions f @ g and g @ f. Find the domain of each composite function. Are the two composite functions equal? f(x) = x^2 − 1 g(x) = −x

melodykap 2020-10-18 Answered
Find the composite functions fg and gf. Find the domain of each composite function. Are the two composite functions equal?
f(x)=x21
g(x) = −x
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Expert Answer

i1ziZ
Answered 2020-10-19 Author has 92 answers

To find the composite function, fg and gf and also their respective domains.
Solution:
The functions are f(x)=x21 and g(x)=x.
The function fg can be evaluated as,
fg=f(g(x))
=f(x)
=(x)21
=x21
The function gf can be evaluated as,
gf=g(f(x))
=g(x21)
=(x21)
=x2+1
The obtained composite function are not equal. And the domain for both the function is complete real numbers as it is defined for each value of x.

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