Consider f : R `rarr (-9 ,oo)` given by f(x) = `5x^(2)+ 6x-9` . Prove that f is invertible with
`f^(-1) (y) = ((sqrt(54+5y)-3)/(5))`
where `R^(+)` is the set of all positive real numbers.

Consider f: R_(+) [4, oo] is given by f(x)= x^(2) + 4. Show that f is invertible with the inverses f^(-1) of f given by f^(-1)(y) = sqrt(y-4) , where R_(+) , is the set of all non-negative real numbers.

Consider f:R_(+) to [-5, oo) given by f(x)=9x^(2)+6x-5 . Show that f is invertible with f^(-1)(y)= ((sqrt(y+6)-1)/(3)) . Hence. Find (i) f^(-1)(10)" " (ii) y" if "f^(-1)(y)=(4)/(3) where R_(+) is the set of all non-negative real numbers.

If the function f:[1, oo) rarr [ 1,oo) defined by f(x) = 2^(x(x -1)) is invertible, then find f^(-1) (x).

If F : R rarr R is given by f(x) = (3-x^(3))^(1//3) then find ( fof ) x .

Let A=R-{3/5} Br f:ArarrA defined as f(x)=(3x+2)/(5x-3) . Br show that is invertible, hence find f^-1.

Prove that f:X rarr Y is injective iff f^(-1) (f(A)) = "A for all" A sube X .