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stepan [7]
3 years ago
8

Find the inverse of f(x)=1/(x^3)

Mathematics
1 answer:
Pepsi [2]3 years ago
4 0

Answer:

Step-by-step explanation:

yf(x)^{-1}  = inverse\\f(x)=y \\y = 1/(x^{3} \\Inverse: y=x ------------> x = 1/y^{3}\\y^{3} - \frac{1}{x} = 0\\y^{3} = \frac{1}{x}\\y = \sqrt[3]{\frac{1}{x}} \\y = \frac{\sqrt[3]{1} }{\sqrt[3]{x}} \\y = \frac{1}{\sqrt[3]{x}}

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Answer:

x=\frac{-5+ln9}{3} which appears to be from the list x=ln9-5/3

Step-by-step explanation:

We take the natural logarithm of both sides as the inverse operation to an exponent on e. This allows us to use log rules to rearrange the problem.

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We know that as inverse operations, ln e =1.

(3x+5)(1)=ln9\\3x+5=ln9\\3x=-5+ln9\\\frac{3x}{3}=\frac{-5+ln9}{3}

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You will note that the numerator and denominator have a common factor:

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<em>Comment on the form of the answer</em>

Since you have written your math expressions using words instead of symbols, we assume you can read them more easily that way. So, we have provided the explanation in the form you can most easily understand. (Personally, I prefer math symbols. They are more compact and tend to be less ambiguous.)

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D

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