# find the value of a variable in continuity function

Function $$G(x) = x-\frac{3}{\sqrt{5x+1}} - \sqrt{3x+7}$$

For what value of the constant k is the function continuous on its domain

f(x)( f(x) combine 2 function/equation together)

=g(x) Domain: xE Dg

=k Domain : x = 3

I think k = 4 because when I look at the graph at desmo, g(x) have a hole at (3,4) (i have no reason why) so it is a removable discontinuity, but this question ask me what is value of k to make f(x) a continuity function and we know that k is only available at x = 3(basically just a dot) and there is a hole at (3,4) in g(x) function so I know that k is going to be 4 to fill up the hole to make continuity.

But how do you calculate k values algebrically?

• Where does $k$ appear in the formula? – pepa.dvorak Feb 9 '17 at 18:50
• why sould be a hole at $$x=3$$? – Dr. Sonnhard Graubner Feb 9 '17 at 18:51
• or do you mean $$G(x)=x-\frac{3}{\sqrt{5x+1}-\sqrt{3x+7}}$$? – Dr. Sonnhard Graubner Feb 9 '17 at 18:53
• multiply the numerator and denominator by $$\sqrt{5x+1}+\sqrt{3x+7}$$ – Dr. Sonnhard Graubner Feb 9 '17 at 18:57
• When u go to desmo and enter the equation there is a hole at 3 – Secret Feb 9 '17 at 18:58