Question
Function
Find the inverse
Evaluate the derivative
Find the domain
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h−1(t)=−705704t
Evaluate
h(t)=−5t2×14t3
Simplify
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Evaluate
−5t2×14t3
Multiply the terms
−70t2×t3
Multiply the terms with the same base by adding their exponents
−70t2+3
Add the numbers
−70t5
h(t)=−70t5
In the equation for h(t),replace h(t) with y
y=−70t5
Interchange t and y
t=−70y5
Swap the sides of the equation
−70y5=t
Change the signs on both sides of the equation
70y5=−t
Divide both sides
7070y5=70−t
Divide the numbers
y5=70−t
Use b−a=−ba=−ba to rewrite the fraction
y5=−70t
Take the 5-th root on both sides of the equation
5y5=5−70t
Calculate
y=5−70t
Simplify the root
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Evaluate
5−70t
To take a root of a fraction,take the root of the numerator and denominator separately
5705−t
Multiply by the Conjugate
570×57045−t×5704
Calculate
705−t×5704
Calculate
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Evaluate
5−t×5704
The product of roots with the same index is equal to the root of the product
5−t×704
Calculate the product
5−704t
An odd root of a negative radicand is always a negative
−5704t
70−5704t
Calculate
−705704t
y=−705704t
Solution
h−1(t)=−705704t
Show Solution
