Composition of Functions: Finding g(f-1(x)) with Given Equations

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Homework Help Overview

The discussion revolves around the composition of functions, specifically finding g(f-1(x)) given the functions f(x) and g(x). The original poster provides their approach to finding the inverse of f and subsequently applying g to that inverse.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to find the inverse function f-1(x) and then substitute it into g(x). Some participants question the accuracy of the calculations, particularly regarding signs and numerical results.

Discussion Status

Participants are actively engaging with the original poster's method, with some providing feedback on potential errors in the calculations. There is a recognition of differing answers, indicating that multiple interpretations of the problem are being explored.

Contextual Notes

There is a mention of a sign error and discrepancies in numerical results, suggesting that the discussion is focused on verifying the steps taken in the calculations rather than reaching a definitive solution.

Darknes51986
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Homework Statement



Given: f(x)= 1/3x + 2 and g(x)= 2x2- x + 7

Find: g(f-1(x))

Homework Equations


The Attempt at a Solution



x=1/3y + 2
1/3y= x - 2
y=(x-2)/(1/3)
y=3x-6= f-1(x)

2(3x-6)2 + (3x-6) +7
solved to get..
18x2-69x+71
 
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I got a different answer but your method is correct. You have a sign error somewhere.
 


2(36)- 6+ 7= 72+1= 73, not 71.
 


g(x)= 2x² - x + 7

2(3x-6)² + (3x-6) + 7
 

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