Find f\cdot g and g\cdot f, where f(x)=x^2+1 and g(x)=x+2,

sklicatias

sklicatias

Answered question

2021-11-15

Find fg and gf, where f(x)=x2+1 and g(x)=x+2, are functions from R to R.

Answer & Explanation

Eprint

Eprint

Beginner2021-11-16Added 13 answers

Definitions
Composition of f and g: (fg)(a)=f(g(a))
Solution:
Given: g:RR and f:RR.
f(x)=x2+1
g(x)=x+2
Since f and g are both functions from R to R, fg and gf are also functions from R to R.
Use the definition of composition:
(fg)(x)=f(g(x))=f(x+2)=(x+2)2+1=x2+4x+5
(gf)(x)=g(f(x))=g(x2+1)=(x2+1)+2=x2+3
Result:
(fg)(x)=x2+4x+5
(gf)(x)=x2+3

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