discuss the continuity of the composite function f o g. f(t)=t^2 g(x,y)=6x - 4y o continuous except at (0,0)…

Explanation:

Step1: Recall continuity of composite functions

For a composite function (f\circ g), if (g(x,y)) is continuous at a point ((a,b)) and (f(t)) is continuous at (g(a,b)), then (f\circ g) is continuous at ((a,b)). The function (f(t)=t^{2}) is a polynomial function and is continuous for all real - valued (t). The function (g(x,y)=6x - 4y) is a linear function and is continuous for all ((x,y)\in\mathbb{R}^{2}).

Step2: Determine continuity of (f\circ g)

Since (f(t)) is continuous for all (t\in\mathbb{R}) and (g(x,y)) is continuous for all ((x,y)\in\mathbb{R}^{2}), the composite function (f\circ g(x,y)=f(g(x,y))=(6x - 4y)^{2}) is continuous everywhere.

Answer:

continuous everywhere