MATH 1004 Lecture 2: W-4

• School: Carleton University
• Department: Mathematics
• Course: MATH 1004
• Professor: Glenn Mc Rae

Document Summary

Let f be a given function with d = dom(f ) and r = ran(f ), we say that function. Dom(f ) = ran(f ), dom(f ) = ran(f ) (f f )(x) = x for every x in dom(f ) The graph of inverse function, f , is obtained by re ecting the graph of f about the line y = x. Example find inverse function for f (x) = x3 + 1: derivatives of inverse function df 1 dx df dx (x) = (x) = Inverse of sin x de ned when dom(sin) = ( y = arc sin(x) means that y is an angle whose sin is x. 2 y y = arc sin(x) = sin 1(x) 0 y y = arc cos(x) = cos 1(x) y = arc tan(x) = tan 1(x) x . 2 y y = arc cot(x) = cot 1(x) x 0 y . 4 ): derivatives of inverse trigonometric functions d dx.