Question
Function
Find the inverse
Evaluate the derivative
Find the domain
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h−1(t)=−150322500t
Evaluate
h(t)=−5t2×30t
Simplify
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Evaluate
−5t2×30t
Multiply the terms
−150t2×t
Multiply the terms with the same base by adding their exponents
−150t2+1
Add the numbers
−150t3
h(t)=−150t3
In the equation for h(t),replace h(t) with y
y=−150t3
Interchange t and y
t=−150y3
Swap the sides of the equation
−150y3=t
Change the signs on both sides of the equation
150y3=−t
Divide both sides
150150y3=150−t
Divide the numbers
y3=150−t
Use b−a=−ba=−ba to rewrite the fraction
y3=−150t
Take the 3-th root on both sides of the equation
3y3=3−150t
Calculate
y=3−150t
Simplify the root
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Evaluate
3−150t
To take a root of a fraction,take the root of the numerator and denominator separately
31503−t
Multiply by the Conjugate
3150×315023−t×31502
Calculate
1503−t×31502
Calculate
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Evaluate
3−t×31502
The product of roots with the same index is equal to the root of the product
3−t×1502
Calculate the product
3−1502t
An odd root of a negative radicand is always a negative
−31502t
150−31502t
Calculate
−15031502t
Calculate
−150322500t
y=−150322500t
Solution
h−1(t)=−150322500t
Show Solution
