Show that the signum function `f:RR rarr RR` , given by
`f(x)={(1" if "x gt 0),(0 " if "x = 0),(-1 " if " x lt0):}`
is neither one-one nor onto.

Prove that, the function f: RR rarr RR defined by f(x)=x^(3)+3x is bijective .

If f(x)={(x^3, x gt 0),(0, x=0),(-x^3, x lt0):}

Show that the modulus function f: RR rarr RR , given by f(x)=|x| is neither one-one nor onto Where |x|={(x " when "x ge 0),(-x " when " x lt 0):}

Let the function f: RR rarr RR be given by , f(x)=3x^(2)-14x+10 . Find (i) f^(-1)(4), (ii) f^(-1) (-8)

Prove that the greatest integer function f: RR rarr RR , given by f(x)=[x] , is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

Discuss the continuity of the function f, where f is defined by f(x)={{:(2x," if "x lt 0),(0," if "0 le x le 1),(4x," if "x gt 1):} .

Let t the function f:RR to RR be defined by, f(x)=a^x(a gt0 ,a ne1). Find range of f

Prove that the function f: RR rarr RR defined by, f(x)=sin x , for all x in RR is neither one -one nor onto.

If the function f: RR rarr RR be defined by, f(x)={(x " when "x in QQ ),(1-x " when " x in QQ ):} then prove that , (f o f)=I_(RR) .

Show that the function f:N to N, given by f (1) =f (2) =1 and f (x) =x -1, for every x gt 2, is onto but not one-one.