Question
Function
Find the inverse
Evaluate the derivative
Find the domain
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h−1(t)=−4516t
Evaluate
h(t)=−4t2×8t3×2
Simplify
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Evaluate
−4t2×8t3×2
Multiply the terms
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Evaluate
4×8×2
Multiply the terms
32×2
Multiply the numbers
64
−64t2×t3
Multiply the terms with the same base by adding their exponents
−64t2+3
Add the numbers
−64t5
h(t)=−64t5
In the equation for h(t),replace h(t) with y
y=−64t5
Interchange t and y
t=−64y5
Swap the sides of the equation
−64y5=t
Change the signs on both sides of the equation
64y5=−t
Divide both sides
6464y5=64−t
Divide the numbers
y5=64−t
Use b−a=−ba=−ba to rewrite the fraction
y5=−64t
Take the 5-th root on both sides of the equation
5y5=5−64t
Calculate
y=5−64t
Simplify the root
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Evaluate
5−64t
To take a root of a fraction,take the root of the numerator and denominator separately
5645−t
Simplify the radical expression
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Evaluate
564
Write the expression as a product where the root of one of the factors can be evaluated
532×2
Write the number in exponential form with the base of 2
525×2
The root of a product is equal to the product of the roots of each factor
525×52
Reduce the index of the radical and exponent with 5
252
2525−t
Multiply by the Conjugate
252×5245−t×524
Calculate
2×25−t×524
Calculate
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Evaluate
5−t×524
The product of roots with the same index is equal to the root of the product
5−t×24
Calculate the product
5−24t
An odd root of a negative radicand is always a negative
−524t
2×2−524t
Calculate
4−524t
Calculate
−4524t
Calculate
−4516t
y=−4516t
Solution
h−1(t)=−4516t
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