Inverse Hyperbolic Functions Concepts

The video tutorial explains how to evaluate inverse hyperbolic functions, focusing on the inverse hyperbolic cosine and sine. It introduces the concept of inverse functions, provides formulas for calculation, and demonstrates examples. The tutorial also covers additional inverse hyperbolic functions, their formulas, and domains, ensuring a comprehensive understanding of the topic.

What is the result of the inverse hyperbolic cosine of one?

• 1

• 0

• Undefined

• Infinity

Which formula represents the inverse hyperbolic cosine function?

• ln(x - sqrt(x^2 - 1))

• ln(x - sqrt(x^2 + 1))

• ln(x + sqrt(x^2 - 1))

• ln(x + sqrt(x^2 + 1))

What is the domain of the inverse hyperbolic cosine function?

• 0 to Infinity

• 1 to Infinity

• -Infinity to 1

• -Infinity to Infinity

What is the formula for the inverse hyperbolic sine function?

• ln(x - sqrt(x^2 - 1))

• ln(x + sqrt(x^2 + 1))

• ln(x + sqrt(x^2 - 1))

• ln(x - sqrt(x^2 + 1))

What is the approximate decimal value of the inverse hyperbolic sine of one?

• 0.69315

• 1.00000

• 0.88137

• 1.41421

Which of the following is the formula for the inverse hyperbolic tangent function?

• 1/2 ln((1 + x)/(1 - x))

• 1/2 ln((x + 1)/(x - 1))

• ln(x + sqrt(x^2 - 1))

• ln(x + sqrt(x^2 + 1))

What is the domain of the inverse hyperbolic tangent function?

• 0 to 1

• -1 to Infinity

• -Infinity to Infinity

• -1 to 1

What is the formula for the inverse hyperbolic secant function?

• ln(x + sqrt(x^2 + 1))

• ln(1 + sqrt(1 + x^2))/x

• ln(x + sqrt(x^2 - 1))

• ln(1 + sqrt(1 - x^2))/x

What is the domain of the inverse hyperbolic secant function?

• 0 to 1

• 1 to Infinity

• -Infinity to 0

• -Infinity to Infinity

Which of the following is true about the domain of the inverse hyperbolic cosecant function?

• All real numbers except zero

• Only positive numbers

• Only negative numbers

• All real numbers