Why do we need restrictions on inverse trig functions

The video tutorial explains the concept of inverse functions and why some functions, like y = x^2, are not invertible without restrictions. It discusses the vertical and horizontal line tests to determine invertibility and how adding restrictions can make a function invertible. The tutorial uses the sine function as an example, showing how restricting its domain allows for an inverse to be found. The importance of these restrictions is emphasized to ensure functions are one-to-one and invertible.

Why is the function y = x^2 not invertible without restrictions?

• It fails the vertical line test.

• It is not continuous.

• It fails the horizontal line test.

• It is not a polynomial function.

What is the purpose of adding restrictions to a function?

• To make it pass the vertical line test.

• To make it pass the horizontal line test.

• To make it continuous.

• To make it a polynomial function.

Which trigonometric function is discussed as failing the horizontal line test?

• Cosine

• Sine

• All of the above

• Tangent

What interval is used to restrict the sine function to make it invertible?

• 0 to π

• 0 to π/2

• -π to π

• -π/2 to π/2

Why is it necessary to restrict the sine function to find its inverse?

• Because it is not a continuous function.

• Because it fails the vertical line test without restrictions.

• Because it fails the horizontal line test without restrictions.

• Because it is not a polynomial function.