Functions: Lecture 2

One to One Function

• A function is one-to-one if no two elements in X are mapped to the same values.
• You can use a horizontal line test to check whether a function is one-to-one.

Inverse Function

• A function has inverse if and only if it is one-to-one. (Why?)
• The domain of function f is the range of its inverse. The range of function f is the domain of its inverse. (Why?)
• The graph of a function and its inverse are the reflections of each other along the line y=x (Why?)
• To find the value for which \[f(x)=f^{-1}(x)\], you need to find the intersection between the graph y=f(x) and y=x using G.C. (Why?)

Inverse Trigonometry Functions

• To ensure sin, cosine and tangent functions have inverse, we have to define principle range (restrict their domains)
• Principal range of sin inverse is [ -pi/2, pi/2]
• Principal range of cos inverse is [0, pi]
• Principal range of tan inverse is [-pi/2, pi/2]

G.C.

When you plot the graph of a function in G.C., do you know how to input the domain like (-1,1)

Ans: You input x>-1 and x<1>"and" can be found in 2nd -> Math -> Logic

Tutorial Questions to attempt

You can attend Q2 to Q5 after today's lecture.