Show that `f : [0,1]rarr]0,1]` defined by `f(x)=1/(x^2+1)` is invertible and find `f^-1(x)`.

Show that f : [1,2] rarr[0,1] defined by f(x)= sqrt(4x-x^2-3) is invertible. Hence find the formula for f^-1(x) .

If f:RrarrR defined by f(x)=(3x+5)/2 is an invertible function, then find f^(-1)

Show that the function f : R rarr R defined by f(x)=x^2+4 is not invertible.

Show that f : R-{a} rarr R-{-1} defined by f(x)= (a+x)/(a-x) is invertible. Find the formula for f^-1(x) .

Prove that f : R rarr R, f(x)=4x-5 is invertible and find f^-1(x) .

Let f : R rarr R be defined as f(x)=2x+3 . Show that f is invertible and find f^-1 : R rarr R .

Show that the function f : R rarr R , defined by {(-1,x 0):} is neither one-one nor onto.

Show that the function f : R_0 rarr R_0 defined by f(x)=1/x , where R_0 is the set of nonzero real numbers is bijective.

If f : R rarr R is defined by f(x)=x^2+2 and g : R-{1} rarr R is defined by g(x)=x/(x-1) , find (fog)(x) and (gof)(x) .

If f : R-{-1} rarr R-{1} be defined by f(x)= (x-1)/(x+1) , verify that fof^-1 is an identity function.