Derivatives of inverse trig. functions (1 Viewer)

[xwrathbringerx]

Hey could someone show me how to do:

State the values of x for which the following functions are defined. For each given f(x), find f'(x) stating the maximal domain of the function it defines.

1. f(x) = inverse sin [2abs(x)]

2. f(x) = inverse sin (2x+1)

3. f(x) inverse cos (1-2x)

[Just examples to help me understand this topic more. ]

 

[gckc123]

the range of sin and cos can only in between -1 and 1
Therefore, inverse sin and inverse cos can only take value in between these two values.

For example, we look at 3.
f(x) = inverse cos(1-2x)

For f(x) to be defined,
we must have

-1 <= 1-2x <= 1

-2 <= -2x <= 0

2 >= 2x >= 0

1 >= x >=0

Therefore, f(x) is defined for x in between 0 and 1

Cheers