Examine the function `f(x) = (x^2+5)/(3x+1)` in the domain (1,7) and state its type of discontinuity

Hello from MrBillDoesMath!

The function is continuous on (1,7)

Discussion:

See attached graph. The discontinuity in the function occurs when

3x + 1 =0   =>

x = - (1/3)

but that x value does not lie in the interval  (1.7). So there is no discontinuity on (1,7).    

FYI:  the discontinuity at -1/3 is a non-removable discontinuity

Thank you,

MrB

answer: 60

step-by-step explanation:

1/2a + (2/3×30)   = 50

1/2a + 20 = 50

1/2a = 30

a = 60

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.