INVERSE AND GRAPH

dude sinx and cosx are also periodic functions
so how can we find their inverses

for a function to have inverse it must be one one and onto
so we take principal value of these functions (by convention )

so what is the point in arguing that its inverse id defined on all the values of R

please draw the graph and find the inverse of the first function!!!!!!!!!!

let y=x+sinx
wel take x as 0....
so y=0

since this passes through d origin and its inverse is a mirror image on y=x...... so even tht also pass through 0,0

so we can eliminate option b and c...
now take ∩/2
y=∩/2+1
point is (∩/2,∩/2+1)
find its mirror image on y=x
and try 2 substitue dat point in a and d....one of them will satisfy......

[1][1][1]

dude good analysis with options
but what if the question was without options ?????????

but i think it could be done in a better way
what about the graph?????

so answer is approximately a.....

Approximately because...
i got d point as (∩/2+1,∩/2)

and when i subsituted in 1
y=∩/2+1-cos1
cos1 is approx 1
so y=∩/2

so ans is approx. A

Dunno about the direct method for inverse, but the graph can be found like this....

The graph for y=x is....

and for y=sinx is....

So, the graph for y=x+sin x is......

Inverse of this function is its mirror image in y=x which gives...

This I suppose is the graph for y= x+cosx

So, the inverse is y=x+cosx

@ kalyan
u said

THINK ABOUT THIS AGAIN
THE AMPLITUDE OF SINX WILL ALWAYS REMAIN FROM-1 TO 1 AND X WILL BEGIN 4M -∞ TO ∞

DO READ #6