Find g(4): Solving the Limit Equation

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SUMMARY

The discussion centers on solving the limit equation involving continuous functions f and g, specifically finding g(4) given f(4)=1 and the limit expression lim x-> 4 (6fx - gx)= 1. The user initially rewrites the limit expression and applies direct substitution to find that g(4) should equal 5/4. However, they later realize an error in their calculations, indicating a misunderstanding in the application of limits. The correct approach requires careful attention to the limit definitions and continuity of the functions involved.

PREREQUISITES
  • Understanding of limit definitions in calculus
  • Knowledge of continuity in functions
  • Familiarity with direct substitution in limit problems
  • Basic algebraic manipulation skills
NEXT STEPS
  • Review the properties of continuous functions and their limits
  • Study the application of the epsilon-delta definition of limits
  • Practice solving limit problems involving multiple functions
  • Learn about common pitfalls in limit calculations and how to avoid them
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Students studying calculus, mathematics educators, and anyone looking to deepen their understanding of limits and continuity in function analysis.

Rasine
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If f and g are continuous functions with f(4)=1 and lim x-> 4 (6fx - gx)= 1 find g(4)

i cam rewrite this as lim x-> 4 (6f) - lim x-> 4 gx =1

so i know that fx is defined at 4 so it has a limit and that by direct substution the limit of fx= 1

so if i replace 1 with the lim of fx i have 1- lim x-> 4 gx=1

and by using direct subustion again i can find g(4) which is the limit of gx

i solve and get 5/4 for the lim of gx which should be g(4) but that is not right

can someone please tell me where i am going wrong?
 
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How did you get 5/4?
 
n/m i just noticed what i was doing wrong
 

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