Determine whether each function is continuous xvalues Justif

Determine whether each function is continuous x-value(s). Justify using the continuity test. If di the type of discontinuity as Infinite, jump, or ref f(x) = x^2 - 3x; x+4. f(x) = squareroot 2x-4; x =10 f(x) = x/x divided 7 ; x = 0 and x= 7 f(x) = x/x^2 - 4 ; x = 2 and x = 4 f(x) = 3x-1 if x less than 2x if x 1 : x =1

Solution

27)f(x)=x^2 -3x

lim_x->4^-f(x)

=lim_x->4^-x^2 -3x

=4^2 -3*4

=16-12

=4

lim_x->4⁺f(x)

=lim_x->4⁺x^2 -3x

=4^2 -3*4

=16-12

=4

f(4)=4^2 -3*4

=16-12

=4

lim_x->4^-f(x)=f(4)=lim_x->4⁺f(x), so function is continous at x =4

........................................................

28)f(x)=(2x -4)

lim_x->10^-f(x)

=lim_x->10^-(2x-4)

=(2*10-4)

=(20-4)

=16

=4

lim_x->10⁺f(x)

=lim_x->10⁺(2x-4)

=(2*10-4)

=(20-4)

=16

=4

f(10)=(2*10-4)

=(20-4)

=16

=4

=4

lim_x->10^-f(x)=f(10)=lim_x->10⁺f(x), so function is continous at x =10