Find the value of constant K that makes the function below continuous at x = 5?? (x^2-5x)/(x-5) xequal to 5

Question

Find the value of constant K that makes the function below continuous at 
x = 5??
          (x^2-5x)/(x-5)       x<5
f(x)          kx-3                 x>equal to 5

anonymous · Answer

This is a lot like the other question. For f(x) to be continuous at x=5, all function parts around there must be equal at x=5.

So to the left hand side of x, you have:
$$f(x) = \frac{x^2-5x}{x-5}$$You need to solve for x=5. (tip: try factoring the numerator)

The next step is to say that all parts of the function have to be equal:
$$\frac{x^2-5x}{x-5}=kx-3 \text{ ; x=5}$$

anonymous · Answer

ok so when i factor the equation it comes to just being x. is that right?

anonymous · Answer

It is indeed!

anonymous · Answer

yay i got it! 8/5. thank youu