SOLUTION: Let f(x) = 2x + 3. Find values for a and b such that the equation f(ax + b) = x is true for all values of x. I've found f(ax + b) and tried to rearrange for b and solve for a by

Question 824890: Let f(x) = 2x + 3. Find values for a and b such that the equation f(ax + b) = x is true for all values of x.
I've found f(ax + b) and tried to rearrange for b and solve for a by substitution but that doesn't work. I was given a hint that if two polynomials in the variable x are equal for all values of x, then the corresponding coefficients are equal.
Please help me solve this, thank you in advance.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
f(ax+b) = 2 * (ax+b) + 3 = 2ax+2b+3, now
if a = 1/2 and b = -3/2 then
2*(1/2)*x +2*(-3/2)+3 = x for all values of x

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