I must have made a mistake in finding the composite functions f circ g and g circ f,because I notice that f circ g is not same function as g circ f

SchachtN

SchachtN

Answered question

2021-09-06

I must have made a mistake in finding the composite functions fgandgf, because I notice that fg is not the same function as gf.Determine whether the statement makes sense or does not make sense, and explain your reasoning.

Answer & Explanation

Alix Ortiz

Alix Ortiz

Skilled2021-09-07Added 109 answers

A composite function is function which is formed when one function is substituted into another function.
f(g(x)) is composite function that is formed when g(x) is substituted for x in f(x).
g(f(x)) is composite function that is formed when f(x) is substituted for x in g(x).
So, it is not necessary that f(g(x))=g(f(x))
Example: If f(x)=x+5andg(x)=3x2
(fg)(x)=f(g(x))
=3x2+5
(gf)(x)=g(f(x))
=g(x+5)
=3(x+5)2
=3(x2+10x+25)
=3x2+30x+75
Therefore, (fg)(x)(gf)(x)
So, it is not necessary that f(g(x))=g(f(x)).
Hence, it is not necessary that if (fg)(x)(gf)(x) then there is mistake in finding composite function. So, statement doesn't make any sense.

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