Letf(x) = 4x + 5.Find values for a and b such that the equationf(ax + b) = xis true for all values of x. Hint: Use the fact that if two polynomials (in the variable x) are equal for all values of x, then the corresponding coefficients are equal.

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter5: Factoring Polynomials
Section5.4: Multiplying Binomials Mentally
Problem 3E
Question

Let
f(x) = 4x + 5.
Find values for a and b such that the equation
f(ax + b) = x
is true for all values of x. Hint: Use the fact that if two polynomials (in the variable x) are equal for all values of x, then the corresponding coefficients are equal.

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