Question

is this piecewise function continuous at x=3?? f(x)=ln3x f(x)=xln3
please help thanks!

Answer 1

Just check if the two pieces are equal at x=3.

Answer 2

that's all? thanks! :)

Answer 3

Yup :) if they are not equal, there is a jump from one value to another at x=3, so it's discontinuous.

Answer 4

do the restrictions matter? for f(x)=ln3x 0<x<=3 and for f(x)=xln3 3<x<=4

Answer 5

Yeah they could matter, I assumed that the pieces switched at x=3 since that was the question. If they would have switched at x=2 say, then it would have been continuous at x=3 since the function would have been in the middle of the \(x\ln3\) segment which is continuous.