`f(x)={3-x , xlt=1 2x , x gt1`

f(x)={(x+1,; xlt1), (2x-3,; xgeq1):}, evaluate lim_(x rarr 1)f(x).

Consider the function f(x)={2x+3,xlt=1 -x^2+6,x >1

Find lim_(xrarr0)f(x)a n d(lim)_(x->1)f(x),""""w h e r e""""f(x)=[2x+3, xlt=0 3(x+1), x >0

Consider the function f(x)={2x+3,xlt=1-x^2+6,x >1

Consider the function f(x)={2x+3,xlt=1-x^2+6,x >1

Find the complete set of values of alpha for which the function f(x) = {(x+1,xlt1 alpha , x =1 , is strictly increasing x=1 x^(2)-x+3,xlt1

Find the complete set of values of alpha for which the function f(x) = {(x+1,xlt1 alpha , x =1 , is strictly increasing x=1 x^(2)-x+3,xlt1

If f(x)={m x+1,xlt=pi/2sinx+n ,x >pi/2 is continuous at x=pi/2, then

Show that f(x)={1+x^2,if0lt=xlt=1 and 2-x if x >1 is discontinuous at x=1