How to find (g@f)(-2+x) given g(x)=2x-2 and f(x)=x^2+3x?

mamounette59cpg

mamounette59cpg

Answered question

2023-01-20

How to find You can't use 'macro parameter character #' in math mode and f(x)=x2+3x?

Answer & Explanation

wolfnightswimfdi

wolfnightswimfdi

Beginner2023-01-21Added 9 answers

Finding a expression for is the first step (g ○ f ), which can also be written as g(f(x)).
To do this substitute x = f(x) into g(x)
g(f(x))=g(x2+3x)=2(x2+3x)2
g(f(x))=2x2+6x2
To evaluate (g ○ f)(-2 +x) substitute x = - 2 +x into g(f(x))
(g(f(2+x))=2(2+x)2+6(2+x)2
=2(44x+x2)12+6x2
=88x+2x212+6x2=2x22x6

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