Inverse Trig. ratio- fitpatrick 3U (1 Viewer)

[lsdpoon1337]

I'm finding this question quite hard:

Ch. 26b), Q10, fitzpatrick

Given f(x)= sin (2x-3) for all x, write down the range of f. Show that a restriction of f, namely F, defined on [1,2], has an inverse F(-1). Find the rule of F(-1), stating its domain and range.

Thanks

 

[proringz]

I'm finding this question quite hard:
Ch. 26b), Q10, fitzpatrick

Given f(x)= sin (2x-3) for all x, write down the range of f. Show that a restriction of f, namely F, defined on [1,2], has an inverse F(-1). Find the rule of F(-1), stating its domain and range.
Thanks

Range: 1 <= y <= 1
To show it has an inverse, show that between x = 1 and x = 2, the f'(x) is only decreasing or increasing. Hence, show it has same sign.
To find inverse replace let f(x) = y and replace the y with x and the x with y. Rearrange, and there u should have your inverse function.
The domain of inverse is the range of the original function. So the domain of the inverse is 1<= 2x-3 <= 1 (add 3 then divide by 2) so Domain: -3/2 <= x <= 3/2 and the range is -pi/2 <= y <= pi/2