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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?

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

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