
Inverse Functions of Hyperbolic Cosine

Interactive Video
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Mathematics
•
11th - 12th Grade
•
Hard

Patricia Brown
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in finding the inverse function of cosh x?
Swap x and y
Complete the square
Multiply both sides by 2
Take the logarithm of both sides
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
After swapping x and y, what expression do we get for x?
x = (e^y - e^-y) / 2
x = (e^y + e^-y) / 2
x = e^y + e^-y
x = e^y - e^-y
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What operation is performed after multiplying by 2 in the derivation?
Multiply by e^y
Divide by e^y
Subtract x from both sides
Add 1 to both sides
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of completing the square in this derivation?
To simplify the equation
To find the roots of the equation
To isolate e^y
To eliminate the square root
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is the domain of cosh x restricted to x ≥ 0?
To eliminate negative values
To simplify the equation
To ensure the function is one-to-one
To ensure the function is many-to-one
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of taking the logarithm of both sides in the final derivation?
It simplifies the equation
It eliminates the square root
It isolates x
It provides the inverse function
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What symmetry property is used in the final derivation?
No symmetry is used
Symmetry about the origin
Symmetry about the y-axis
Symmetry about the x-axis
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