The function f is defined by `f(x)={(,1-x,x lt 0),(,1,x=0),(,x+1,x gt 0):}`
Draw the graph of f(x).

The function is defined by f(x) = {(kx+1,if, x lepi),(cos x,if, x gt pi):} at x = pi .

Show that the signum function f : R to R given by f(x) = {(1, if, x gt 0),(0, if, x = 0),(-1, if, x lt 0):} is neither one-one nor onto.

Let f : R to R be the Signum Function defined as f (x) = {{:(1",", x gt 0), ( 0"," , x =0), ( -1 "," , x lt 0):} and g : R to R be the Greatest Integer Function given by g (x) = [x], where [x] is greatest integer less than or equal to x. Then does fog and gof coincide in (0,1] ?

Is the function f defined by f(x) = {{:(x," if "x le 1),(3," if "x gt 1):} continuous at x= 0 ? At x=1? At x=2? .

Let f:[0.1] rarr[0,1] and g:[0,1] rarr[0,1] be two functions defined by f(x)=(1-x)/(1+x) and g(x)=4 x(1-x) , then f . o g(x)=

For what value of lambda is the function defined by f(x)={{:(lambda(x^2 -2x)",",ifxle0),(4x +1",",ifx gt0):} continuous at x = 0 ?

Is the function defined by f(x)={{:(x+5," if "x le1),(x-5," if "x gt 1):} a continuous function?