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soldier1979 [14.2K]

3 years ago

5

X^3-64=0 Solve the equation

1 answer:

solniwko [45]3 years ago

8 0

X^3 - 64 = 0

We want to solve for x. Start by getting x by itself on one side.
We can do this by adding 64 to both sides of the equation.

x^3 = 64

Now, to get rid of the 3rd power that x is raised to, we can raise both sides to the 1/3 power

(x^3)^1/3 = 64^1/3

(x^3)^1/3 is the same as x

So x = 64^(1/3) and 64^(1/3) = 4

So x = 4 :)

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The functions are inverses; f(g(x)) = x ⇒ answer D

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* <em>Lets explain how to find the inverse of a function</em>

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∵ f(x) = y

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- Change y by $f^{-1}(x)$

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* <em>Now lets find f(g(x))</em>

- To find f(g(x)) substitute x in f(x) by g(x)

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∴ $f(g(x))=\sqrt{(x^{2}+3)-3}=\sqrt{x^{2}+3-3}=\sqrt{x^{2}}=x$

∴ <u><em>f(g(x)) = x</em></u>

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- Let h(x) = y

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- Exchange x and y

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- Take √ for both sides

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∵ x ≥ 0

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∴ $\sqrt{\frac{x+1}{3}}=y$

- replace y by $h^{-1}(x)$

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