Question
Function
Find the inverse
Evaluate the derivative
Find the domain
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v−1(t)=103100t
Evaluate
v(t)=5t2×2t×1
Simplify
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Evaluate
5t2×2t×1
Rewrite the expression
5t2×2t
Multiply the terms
10t2×t
Multiply the terms with the same base by adding their exponents
10t2+1
Add the numbers
10t3
v(t)=10t3
In the equation for v(t),replace v(t) with y
y=10t3
Interchange t and y
t=10y3
Swap the sides of the equation
10y3=t
Divide both sides
1010y3=10t
Divide the numbers
y3=10t
Take the 3-th root on both sides of the equation
3y3=310t
Calculate
y=310t
Simplify the root
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Evaluate
310t
To take a root of a fraction,take the root of the numerator and denominator separately
3103t
Multiply by the Conjugate
310×31023t×3102
Calculate
103t×3102
Calculate
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Evaluate
3t×3102
The product of roots with the same index is equal to the root of the product
3t×102
Calculate the product
3102t
103102t
Calculate
103100t
y=103100t
Solution
v−1(t)=103100t
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