FUCTIONS DOUBT 2222222222

[1357913579]

I HAVE A DOUBT ON FUNCTIONS TO KNOW WHETHER A FUNCTION IS ONE ON ONE OR NOT SO IS IT BY GETTING FF-1 SAME AS F-1F AND DOES F(X)= X^2 + 1 ONE-ONE FUNCTION SAM E GOES FOR F(X) = X^2 - 3X AND FOR COS SIN AND TAN ARE ONE-ONE IF NOT THEN IN WHAT RANGE THOSE ARE ONE-ONE THANKS

 

[destined007]

One to one function gives only one value of x with the given value of y in a certain range. Only one to one functions have inverse.
F(X)= X^2 + 1 and F(X) = X^2 - 3X are one to one (over restricted range) because they both have inverse.
sin, cos and tan are not one to one in range of 0≤x≤360. However, they can be one to one in range like 0≤x≤90.

 

[destined007]

here:

 

[1357913579]

WHAT ABOUT TAN AND COSINE

 

[destined007]

For sin -90≤x≤90 for inverse to be possible.
cos has same concept as sin. Just draw the graphs and you will come up with an answer after all these explanation, i am sure. (range is 0≤x≤180. In this range of cos inverse is possible)
For tan, the range is -90≤x≤90. look at the graph of tan.
there can be other ranges but stick to these for the time being.

 

[1357913579]

WHAT ABOUT X^3 - 2

 

[destined007]

y=x^3 -2
(y+2)^1/3=x
f-1(x)=(x+2)^1/3

This is a simple cubic equation. However, inverse of cubic equation in the form ax^3+bx^2+cx+d is not in the syllabus.

 

[1357913579]

SO THESE TYPE OF QUESTION WILL NOT COME LIKE DETERMINE WHICH ONES ARE ONE-ONE FUNCTIONS X^3 - 2, x^3-3x, x^9 no range is specified in the question i guess they mean for all ranges.

 

[destined007]

No I have never seen such a question in the past paper.
When you complete a topic do it's past papers so that you get familiar with the type of question expected from that topic.