Show that the Signum Function `f:RrarrR`, given by :
`f(x)={{:("1, if "xgt0),("0, if "x=0),("-1, if "xlt0):}` is neither one-one nor onto.

Show that the Signum Function f" ": R->R , given by f(x)={1,""if""""x"""">""""0 0,""""if""""x=0-1, if""""x<0 is neither one-one nor onto.

Show that the Signum function f:R rarr R , given by f(x)={[1,x>00,x=0-1,x<0]) is neither one-one nor onto

Prove that the function f:RrarrR given by: f(x) = 5x is one-one and onto.

Show that the function f(x) given by f(x)={xsin1/x ,x!=0 0,x=0

If f(x)={(x-1",",xlt0),(1/4",",x=0),(x^2",",xgt0):} , then

Show that the function f(x) defined by : f(x)={{:((sinx)/x+cosx", "xgt0),(2", "x=0),((4(1-sqrt(1-x)))/x", "xlt0):} is continuous at x = 0.

Show that the function f:RrarrR given by : f(x)=ax+b , where a, binR, ane0 one one and onto.

Show that the modulus function f:R rarr R , given by f(x)=|x| is neither one-one nor onto.

Show that the Modulus Function f" ": R->R , given by f" "(x)" "=" "|" "x" "| , is neither one-one nor onto, where |" "x" "| is x, if x is positive or 0 and |" "x" "| is " "x , if x is negative.

Discuss the continuity of the function f, where f is defined by : f(x)={{:(2x", if "xlt0),(0", if "0lexle1),(4x", if "xgt1):}