Exploring Inverse Functions in IB Maths

This video tutorial covers inverse functions, explaining their notation and how to find them using both graphical and analytical methods. It highlights the importance of understanding that inverse functions are not simply reciprocals. The tutorial demonstrates how to reflect graphs across the line y=x to find inverses and explains the domain and range swap that occurs with inverse functions. An example is provided to illustrate solving inverses analytically, emphasizing the process of switching x and y values and solving for y.

What notation is used to denote an inverse function of f?

• f(x)^-1

• f^-1(x)

• 1/f(x)

• f(x+1)

What line do you reflect across to find the inverse of a function graphically?

• y = -x

• y = x

• x = y

• x = -y

What does the vertical line test determine?

• If a function is invertible

• If a function is continuous

• If a function is differentiable

• If a function is one-to-one

What is the correct reflection of the point (2,4) across the line y = x?

• (4,2)

• (-4,-2)

• (-2,-4)

• (2,4)

When finding the inverse analytically, what is the first step?

• Solve for x

• Switch x and y

• Graph the function

• Find the derivative

What happens to the domain and range when taking the inverse of a function?

• They remain unchanged

• They become infinite

• They become undefined

• They swap

How do you solve for y when finding the inverse of f(x) = e^x + 3?

• y = e^(x - 3)

• y = ln(x - 3)

• y = ln(x) + 3

• y = e^(x + 3)

What is the domain of the function f(x) = e^x + 3?

• x >= 3

• All real numbers

• x < 3

• x > 0

What is the range of the inverse function of f(x) = e^x + 3?

• y <= 3

• y > 0

• All real numbers

• y >= 3

What is the inverse function of f(x) = e^x + 3?

• f^-1(x) = e^(x - 3)

• f^-1(x) = e^(x + 3)

• f^-1(x) = ln(x - 3)

• f^-1(x) = ln(x) + 3