An algebra problem by Mark Dave Martin

Algebra Level 2

If f(g(x))=3x+1 and f(x)=3x-2, find g(-2).

-1 -7/3 4 5/2

Mark Dave Martin by Mark Dave Martin , 22, Philippines

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1 solution

Hansraj Sharma
Aug 10, 2014

let g(x)=ax+b
3(ax+b)-2=3x+1 a=1,b=1 so g(x)=x+1 g(-2)=-1

1 Helpful 0 Interesting 0 Brilliant 0 Confused

A much simpler solution which would avoid taking any extra constants would be,

f ( g ( x ) ) = 3 x + 1 ∧ f ( x ) = 3 x − 2 f(g(x))=3x+1~\land~f(x)=3x-2 ⟹ 3 g ( x ) − 2 = 3 x + 1 ⟹ g ( x ) = x + 1 ⟹ g ( − 2 ) = ( − 1 ) \\ \implies 3g(x)-2=3x+1\implies g(x)=x+1 \implies \boxed{g(-2)=(-1)}

Prasun Biswas - 6 years, 4 months ago

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