Given That F(x)=x^2. F(2x-1)=g(2x-5). Prove That G(x)=x^2+8x+16.

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Given that f(x)=x^2. F(2x-1)=g(2x-5). Prove that g(x)=x^2+8x+16.
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I'm not sure is this question under composite function. this is a 2marks proving question.
  • composite functions
  • algebra problems
  • composition of functions
asked Feb 5, 2014 in Algebra 1 Answers by answer comment

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Question: Given that f(x)=x^2. F(2x-1)=g(2x-5). Prove that g(x)=x^2+8x+16. ?

Given: f(x) = x^2

And: f(2x-1) = g(2x-5)

From the given, g(2x-5) = (2x-1)^2

g(2x-5) = {(2x-5) + 4)}^2 = (2x-5)^2 + 8(2x-5) + 16

i.e. g(u) = u^2 + 8u + 16

or, g(x) = x^2 + 8x + 16

answered Feb 5, 2014 by Level 11 User (81.5k points) ask related question comment

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