f(x)=x(x+1)(2x+1) then f(x)-f(x-1)= ?
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The answer is given below :
Given,
f(x) = x(x + 1)(2x + 1)
Now, to find f(x - 1), just replace x by (x - 1).
So,
f(x - 1)
= (x - 1)(x - 1 + 1){2(x - 1) + 1}
= (x - 1)(x)(2x - 2 + 1)
= (x - 1)(x)(2x - 1)
= x(x - 1)(2x - 1)
Now,
f(x) - f(x - 1)
= x(x + 1)(2x + 1) - x(x - 1)(2x - 1)
= x[(x + 1)(2x + 1) - (x - 1)(2x - 1)]
= x[(2x² + x + 2x + 1) - (2x² - x - 2x + 1)]
= x[2x² + 3x + 1 - 2x² + 3x - 1]
= x[6x]
= 6x² [Answer]
Thank you for your question.
Given,
f(x) = x(x + 1)(2x + 1)
Now, to find f(x - 1), just replace x by (x - 1).
So,
f(x - 1)
= (x - 1)(x - 1 + 1){2(x - 1) + 1}
= (x - 1)(x)(2x - 2 + 1)
= (x - 1)(x)(2x - 1)
= x(x - 1)(2x - 1)
Now,
f(x) - f(x - 1)
= x(x + 1)(2x + 1) - x(x - 1)(2x - 1)
= x[(x + 1)(2x + 1) - (x - 1)(2x - 1)]
= x[(2x² + x + 2x + 1) - (2x² - x - 2x + 1)]
= x[2x² + 3x + 1 - 2x² + 3x - 1]
= x[6x]
= 6x² [Answer]
Thank you for your question.
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