Linear functions are functions which satisfy the two properties:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]f(x+y)=f(x)+f(y) \\

f(a*x)=a*f(x) [/itex]

I was wondering how would you show this property was true for multi-variable functions e.g. [itex] f(x,y,z). [/itex] Would it suffice to show [tex] f(x_{1}+x_{2},y,z)=f(x_1,y,z)+f(x_2,y,z) \\ f(a*x,y,z)=a*f(x,y,z)?[/tex] Basically fix all other variables and show the properties are true for one variable, then repeat for the next variable different to the one we chose before.

Or would you have to consider something like [tex] f(x_{1}+x_{2},y_{1}+y_{2},z_1+z_2) \ \text{and} \ f(a*x,a*y,a*z)? [/tex]

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# Linear Functions

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