Find the composite functions f @ g and g @ f. Find the domain of each composite function. Are the two composite functions equalf(x) = 3x + 1 g(x) = −x

Jaden Easton 2021-02-25 Answered

Find the composite functions fg and gf. Find the domain of each composite function. Are the two composite functions equal
f(x)=3x+1
g(x)=x

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Expert Answer

faldduE
Answered 2021-02-26 Author has 109 answers

Consider the function:
f(x)=3x+1,g(x)=x
To calculate (fg)
(fg)(x)=f(g(x))
=3(g(x))+1
=3(x)+1
=3x+1
To calculate (gf)
(gf)(x)=g(f(x))
=g(3x+1)
=(3x+1)
=3x1
To calculate the domain of (fg) and (gf) function, The domain of a function is the set of input values for which the function is real or defined,
Here,The composite function (fg) and (gf) has no undefined points.
Therefore the domain of both composite functions is <x<
Both composite functions are not equal.

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