Which of the following functions are continuous at x=−1 ?g(x)=sin(x+1)f(x)=x−11Choose 1 answer:(A) g only(B) f only(C) Both g and f(D) Neither g nor f
Q. Which of the following functions are continuous at x=−1 ?g(x)=sin(x+1)f(x)=x−11Choose 1 answer:(A) g only(B) f only(C) Both g and f(D) Neither g nor f
Check Function Continuity: To determine if g(x)=sin(x+1) is continuous at x=−1, we need to check if the function is defined at that point and if the limit as x approaches −1 exists and is equal to the function's value at x=−1.
Calculate g(−1): Substitute x=−1 into g(x) to find g(−1). g(−1)=sin((−1)+1)=sin(0)=0. Since the sine function is continuous everywhere, the limit as x approaches −1 of g(x) is also 0.
Check Function Continuity: To determine if f(x)=(x−1)1 is continuous at x=−1, we need to check if the function is defined at that point and if the limit as x approaches −1 exists and is equal to the function's value at x=−1.
Calculate f(−1): Substitute x=−1 into f(x) to find f(−1). f(−1)=((−1)−1)1=−21=−21. Since the function is defined at x=−1 and the denominator is not zero, the function is continuous at that point.
Verify Continuity: Since both g(x) and f(x) are continuous at x=−1, the correct answer is (C) Both g and f.
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