If `f:R to R` is the function defined by `f(x)=4x^(3) +7`, then show that f is a bijection.

Let A = R-{2} and B = R - {1}. If f : A rarr B is a function defined by f(x)= (x-1)/(x-2) then show that f is one-one and onto. Hence, find f^(-1) .

If A = R -{3} and B = R -{1}. Consider the function f:A to B defined by f(x)=(x-2)/(x-3) , for all x in A . Then, show that f is bijective. Find f^(-1)(x) .

If f:RrarrR defined by f(x)=5x-8 for all x inR , then show that f is invertible. Find the corresponding inverse function.

If f is an invertible function, defined as f(x)= (3x-4)/(5) then write f^(-1) (x).

Show that the function f defined by f(x)=|1-x+|x|| , where x is any real number is a continuous function.