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Determine the Continuity of the Composite Function fg where f(t)=1t and f \circ g \text { where } f ( t ) = \frac { 1 } { t } \text { and }

Question 31

Multiple Choice

Determine the continuity of the composite function fg where f(t) =1t and f \circ g \text { where } f ( t ) = \frac { 1 } { t } \text { and } g(x,y) =5x8yg ( x , y ) = 5 x - 8 y


A) continuous except at (0,58) \left( 0 , \frac { 5 } { 8 } \right)
B) continuous for all y58xy \neq \frac { 5 } { 8 } x
C) continuous for all y=58xy = \frac { 5 } { 8 } x
D) continuous except at (85,58) \left( \frac { 8 } { 5 } , \frac { 5 } { 8 } \right)
E) continuous everywhere

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