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Which of the following functions are continuous at x=-3 ? {:[h(x)=(1)/((x+3)^(2))],[g(x)=(x-3)^(3)]:} Choose 1 answer: (A) h only (B) g only (C) Both h and g (D) Neither h nor g

Which of the following functions are continuous at x=−3 x=-3 ?\newlineh(x)=1(x+3)2g(x)=(x−3)3 \begin{array}{l} h(x)=\frac{1}{(x+3)^{2}} \\ g(x)=(x-3)^{3} \end{array} \newlineChoose 11 answer:\newline(A) h h only\newline(B) g g only\newline(C) Both h h and g g \newline(D) Neither h h nor g g

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Q. Which of the following functions are continuous at x=−3 x=-3 ?\newlineh(x)=1(x+3)2g(x)=(x−3)3 \begin{array}{l} h(x)=\frac{1}{(x+3)^{2}} \\ g(x)=(x-3)^{3} \end{array} \newlineChoose 11 answer:\newline(A) h h only\newline(B) g g only\newline(C) Both h h and g g \newline(D) Neither h h nor g g
  1. Function h(x) Analysis: Analyze the function h(x)=1((x+3)2)h(x) = \frac{1}{((x+3)^{2})} to determine if it is continuous at x=−3x = -3. We need to check if the function is defined at x=−3x = -3 and if there are any points of discontinuity around x=−3x = -3. Substitute x=−3x = -3 into h(x)h(x) to see if the function is defined. h(−3)=1((−3+3)2)=10h(-3) = \frac{1}{((-3+3)^{2})} = \frac{1}{0}, which is undefined. Since division by zero is undefined, the function h(x)h(x) has a point of discontinuity at x=−3x = -3.
  2. Function g(x)g(x) Analysis: Analyze the function g(x)=(x−3)3g(x) = (x-3)^{3} to determine if it is continuous at x=−3x = -3. We need to check if the function is defined at x=−3x = -3 and if there are any points of discontinuity around x=−3x = -3. Substitute x=−3x = -3 into g(x)g(x) to see if the function is defined. g(−3)=((−3)−3)3=(−6)3=−216g(-3) = ((-3)-3)^{3} = (-6)^{3} = -216, which is a real number. Since there is a real number result, the function g(x)g(x) is defined at x=−3x = -3 and there are no points of discontinuity.

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