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  • Find the value of k, so that the function <img alt="f(x) =\begin{Bmatrix} kx^{2}+5 & if & x\leq 1 \\ 2& if &x>1 \end{Bmatrix}" src="https://learn.careers360.com/latex-image/?f%28x%29%20%3D%5Cbegin%7BBmatrix%7D%20kx%5E%7B2%7D&plus

Find the value of k, so that the function f(x) =\begin{Bmatrix} kx^{2}+5 & if & x\leq 1 \\ 2& if &x>1 \end{Bmatrix} is continuous at x = 1.

 

 

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f(x) =\begin{Bmatrix} kx^{2}+5 & if & x\leq 1 \\ 2& if &x>1 \end{Bmatrix}

f(x) is continuous at x=1

\\ f(1^+) = f(1^-) \\ 2 = k(1)^{2}+5 \\ k =-3

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