Question

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

Answer 1

Hello from MrBillDoesMath!

Answer:

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