What is triangular number

Mathematics

1 answer:

ELEN [110]3 years ago

5 0

Answer:

Theory

Step-by-step explanation:

A triangular number or triangle number counts objects arranged in an equilateral triangle. The nth triangular number is the number of dots in the triangular arrangement with n dots on a side, and is equal to the sum of the n natural numbers from 1 to n. The sequence of triangular numbers , starting at the 0th triangular number, is 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666...

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#6 is the question, are these two functions inverse’s

olya-2409 [2.1K]

I will find the inverse function of f(n) to see if it is g(n).

$f(n) = 2(n - 2)^3$

$y = 2(x - 2)^3$

$x = 2(y - 2)^3$

$(y - 2)^3 = \dfrac{x}{2}$

$y - 2 = \sqrt[3]{\dfrac{x}{2}}$

$y = \sqrt[3]{\dfrac{x}{2}} + 2$

$y = \sqrt[3]{ \dfrac{x}{2} } \times \sqrt[3]{ \dfrac{4}{4}} + 2$

$y = \sqrt[3]{\dfrac{4x}{8}} + 2$

$y = \dfrac{ \sqrt[3]{4x }}{2} + 2$

$g(n) = \dfrac{\sqrt[3]{4n}} {2} + 2$

The inverse function of f(n) is indeed g(n), so f(n) and g(n) are inverse functions.

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it will be 50000

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