Substituting Functions: Simplifying Multivariate Expressions

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SUMMARY

The discussion centers on the substitution of functions in multivariate expressions, specifically examining the function T(x,y,z) = xy - z and the relationship z = x + y. When substituting z into T, the resulting expression simplifies to T(x,y) = xy - (x + y), effectively eliminating the variable z from the function. This confirms that T becomes a function of only x and y after substitution, demonstrating a fundamental principle in function simplification.

PREREQUISITES
  • Understanding of multivariate functions
  • Familiarity with function substitution
  • Basic algebraic manipulation skills
  • Knowledge of mathematical notation and terminology
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  • Study the concept of function composition in mathematics
  • Explore algebraic simplification techniques
  • Learn about the implications of variable elimination in calculus
  • Investigate applications of multivariate functions in real-world scenarios
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Mathematicians, students studying algebra and calculus, educators teaching function theory, and anyone interested in simplifying complex mathematical expressions.

fred2028
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This is more of a concept question, so the template is not followed.

Say you're given

T(x,y,z) = xy-z

And

z = x+y

Basically, T is a function of x, y, and z while z is a function of x and y. If we substitute z into T, would T become T(x, y) or stay T(x, y, z)?
 
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Your function would become T(x,y)
 
rock.freak667 said:
Your function would become T(x,y)

OK thanks!
 

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