Question
Function
Find the inverse
Evaluate the derivative
Find the domain
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p−1(x)=−5325x
Evaluate
p(x)=−3x3−2x2×x
Simplify
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Evaluate
−3x3−2x2×x
Multiply
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Multiply the terms
2x2×x
Multiply the terms with the same base by adding their exponents
2x2+1
Add the numbers
2x3
−3x3−2x3
Collect like terms by calculating the sum or difference of their coefficients
(−3−2)x3
Subtract the numbers
−5x3
p(x)=−5x3
In the equation for p(x),replace p(x) with y
y=−5x3
Interchange x and y
x=−5y3
Swap the sides of the equation
−5y3=x
Change the signs on both sides of the equation
5y3=−x
Divide both sides
55y3=5−x
Divide the numbers
y3=5−x
Use b−a=−ba=−ba to rewrite the fraction
y3=−5x
Take the 3-th root on both sides of the equation
3y3=3−5x
Calculate
y=3−5x
Simplify the root
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Evaluate
3−5x
To take a root of a fraction,take the root of the numerator and denominator separately
353−x
Multiply by the Conjugate
35×3523−x×352
Calculate
53−x×352
Calculate
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Evaluate
3−x×352
The product of roots with the same index is equal to the root of the product
3−x×52
Calculate the product
3−52x
An odd root of a negative radicand is always a negative
−352x
5−352x
Calculate
−5352x
Calculate
−5325x
y=−5325x
Solution
p−1(x)=−5325x
Show Solution
