Exercise · ZW-FUNCTION-OF-SEVERAL-VARIABLES-008 · ★★☆ Intermediate
If \(f(x,y)=x^2y\), what is \(\dfrac{f(2x,2y)}{f(x,y)}\) when \(f(x,y)\ne0\)?
Choose one option.
Show answer
- D. \(8\)
Explanation
\(f(2x,2y)=(2x)^2(2y)=8x^2y\), so the quotient is \(8\). Three factors of \(2\) are multiplied, one for each degree.
Review the concept: Function of several variables
A function of several variables \(f\) assigns to each point \(\mathbf x=(x_1,\dots,x_n)\) of a set \(D\subseteq\mathbb R^n\), its domain, a single real number.
\[f:D\subseteq\mathbb R^n\to\mathbb R\]
More practice problems: function of several variables
- ZW-FUNCTION-OF-SEVERAL-VARIABLES-001 If f(x,y)=x^2+3y, compute f(2,1).
- ZW-FUNCTION-OF-SEVERAL-VARIABLES-002 If f(x,y,z)=xyz-z, compute f(1,2,3).
- ZW-FUNCTION-OF-SEVERAL-VARIABLES-003 What is the domain of f(x,y)=√4-x^2-y^2?
- ZW-FUNCTION-OF-SEVERAL-VARIABLES-004 Find the domain of f(x,y)=ln (x-y).
- ZW-FUNCTION-OF-SEVERAL-VARIABLES-005 What is the range of f(x,y)=x^2+y^2?
- ZW-FUNCTION-OF-SEVERAL-VARIABLES-006 Which points belong to the domain of f(x,y)=(1)/(x^2+y^2-1)?
- ZW-FUNCTION-OF-SEVERAL-VARIABLES-007 The graph of a function f(x,y) of two variables is a subset of:
- ZW-FUNCTION-OF-SEVERAL-VARIABLES-009 What is the domain of f(x,y)=√ x+ln y?
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