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2 years ago

Given the function g(x) = 41x3 + a for some constant a, which describes the inverse function

Mathematics

1 answer:

Paha777 [63]2 years ago

7 0

Answer:

When we have a function g(x) such that:

g(x) = y.

Then the inverse, h(x), must be such that:

h(y) = x.

This means that:

g( h(x) ) = x

h( g(x) ) = x.

In this case, g(x) = 41*x^3 + a.

Then:

g( h(x)) = x = 41*h(x)^3 + a.

Now we can solve it for h(x).

x - a = 41*h(x)^3

(x - a)/41 = h(x)^3

∛( (x -a)/41 ) = h(x)

h(x) is the inverse function of g(x).

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Complete Question

Let P (n) be the statement that a postage of n cents can be formed using just 4-cent stamps and 7-cent stamps. The parts of this exercise outline a strong induction proof that P (n) is true for n ≥ 18.

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Answer:

P(18) is true

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Step-by-step explanation:

a. When n = 18

18 cents can be formed using two 7cents and one 4cents

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(B) If we reflect ΔABC across the origin, then also the image will coincide with ΔA'B'C' and so this transformation can also take place.

(C) If we rotate ΔABC through 180° clockwise about the origin, the we will see the image will be same as ΔA'B'C'. Hence, this transformation can also take place.

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