Holiday Problem #4

Algebra Level 2

Given the two functions f ( x ) = x 2 − x + 2 , g ( x ) = a x + b f(x) = x^2 - x + 2, g(x) = ax + b satisfying the equation

f ( g ( x ) ) = 9 x 2 − 3 x + 2 f(g(x)) = 9x^2-3x+2

Find the number of possible ordered pairs of ( a , b ) (a,b) which satisfy this relationship.


The answer is 2.

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Parth Lohomi by Parth Lohomi , 20, India

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1 solution

Rohan Bansal
Mar 9, 2015

(ax+b)^2 - (ax+b) + 2 = 9x^2 - 3x + 2

a^2x^2 + x(2ab - a) + (b^2 - b +2)=9x^2 - 3x +2

Comparing coefficients

a=3,b=0

a=-3,b=1

2 Helpful 0 Interesting 0 Brilliant 0 Confused

@Parth Lohomi Please select the level of your problems responsibly. Please do not make me lower your level so that you can't set all of your problems as level 5.

Calvin Lin Staff - 6 years, 3 months ago

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