Question
Function
Find the inverse
Evaluate the derivative
Find the domain
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f−1(c)=190336100c
Evaluate
f=95c3×2
Simplify
f=190c3
Interchange c and y
c=190y3
Swap the sides of the equation
190y3=c
Divide both sides
190190y3=190c
Divide the numbers
y3=190c
Take the 3-th root on both sides of the equation
3y3=3190c
Calculate
y=3190c
Simplify the root
More Steps

Evaluate
3190c
To take a root of a fraction,take the root of the numerator and denominator separately
31903c
Multiply by the Conjugate
3190×319023c×31902
Calculate
1903c×31902
Calculate
More Steps

Evaluate
3c×31902
The product of roots with the same index is equal to the root of the product
3c×1902
Calculate the product
31902c
19031902c
Calculate
190336100c
y=190336100c
Solution
f−1(c)=190336100c
Show Solution

Solve the equation
Solve for c
Solve for f
c=190336100f
Evaluate
f=95c3×2
Simplify
f=190c3
Swap the sides of the equation
190c3=f
Divide both sides
190190c3=190f
Divide the numbers
c3=190f
Take the 3-th root on both sides of the equation
3c3=3190f
Calculate
c=3190f
Solution
More Steps

Evaluate
3190f
To take a root of a fraction,take the root of the numerator and denominator separately
31903f
Multiply by the Conjugate
3190×319023f×31902
Calculate
1903f×31902
Calculate
More Steps

Evaluate
3f×31902
The product of roots with the same index is equal to the root of the product
3f×1902
Calculate the product
31902f
19031902f
Calculate
190336100f
c=190336100f
Show Solution
