Simplifying Exponents: Tips and Tricks for Solving Complex Equations

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SUMMARY

The discussion focuses on solving the composite function f(g(x)) where f(x) = 1/√x and g(x) = x² - 5. The user expresses confusion about squaring the expression "square root of x over 2x," which is not relevant to the problem at hand. The correct approach involves substituting g(x) into f(x) to find f(g(x)). The user also highlights the challenge of solving these problems without a calculator, which adds to their confusion.

PREREQUISITES
  • Understanding of composite functions
  • Knowledge of square roots and their properties
  • Familiarity with polynomial functions
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the concept of composite functions in detail
  • Learn about the properties of square roots and their applications
  • Practice polynomial function transformations
  • Explore algebraic techniques for simplifying complex expressions
USEFUL FOR

Students in algebra courses, mathematics educators, and anyone looking to improve their skills in solving composite functions and simplifying expressions without calculators.

dustinj.11
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Homework Statement



Attached is the problem, I don't like the math editor used on this site, so its a pdf. The only real problem I have is how to is how do you square a problem like square root of x over 2x?
 

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dustinj.11 said:

Homework Statement



Attached is the problem, I don't like the math editor used on this site, so its a pdf. The only real problem I have is how to is how do you square a problem like square root of x over 2x?

Welcome to the PF.

Since you are given [tex]f(x) = \frac{1}{\sqrt{x}}[/tex]

and [tex]g(x) = x^2 - 5[/tex]

what is f(g(x))? Wouldn't you substitute the g(x) term into the f(x) equation? Where do you get "square root of x over 2x"?
 
Thanks for the help, bt the answers were multiple choice, and as it turns out the correct choice wasn't there. Thats what confused me. Sorry if i seemed a little confused, just I was bred on a calculator, and now my calc ab teacher won't let us use any type of calculator. So, 90% of the time my brain is fried.
 

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