Question

- Let f be the function from R to R defined by f(x)=x2.Find
a) f−1({1}).  

b) f−1({x | 0 < x < 1}

c) f−1({x|x>c) f−1({x|x>4}).

-Show that the function f (x) = e x from the set of real numbers to the set of real numbers is not invertible  but if the codomain is restricted to the set of positive real numbers, the resulting function is invertible.

Answer 1

====================================ANSWER============================================

ANSWER A) -

{ 1, - 1 }   

ANSWER B) -

   { x | − 1 < x < 0 v 0 < x < 1 }

ANSWER C) -

   { x | x > 2 v x < − 2 }

prove -

Invertible means 1 to 1 , onto and the element of negative real number.
f(x)= ex is a closely growing function and  domain must be positive infinity.

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