`f(x)={{:(x^(2)", "xle2),(8-2x", "2ltxlt4),(4", "xge4):}`

Find the points at which f is discontinuous. At which of these points f is continuous from the right, from the left, or neither? Sketch the graph of f. f(x)={{:(2x+1", ""if "xle-1),(3x", ""if "-1ltxlt1),(2x-1", ""if "xge1):}

Let f(x)={{:(0", ""if "xlt0),(x^(2)", ""if "0lexlt2),(4", ""if "xge2):} . Graph the function. Show that f(x) continuous on (-oo,oo) .

Sketch graph and identify the values of x for which lim f(x) exists. f(x)={:{(x^2,x le2),(8-2x,2 lt x lt 4),(4,x ge4):}

A function f [-3, 7] rarr R is defined as follows f(x) = {{: (4x^(2) - 1, " " -3 le x lt 2 ),(3x -2, " " 2 le x le 4 ),(2x -3 , " " 4 lt x lt 7):} Find (i) f (5) + f(6) (ii) f(1) - f(-3) (iii) f(-2)-f(4) (iv) (f(3)+ f(-1))/(2 f(6) - f(1))

If f(x)={{:(-e^(-x)+k,",",xle0),(e^(x)+1,",",0ltxlt1),(ex^(2)+lambda,",",xge1):} is one-one and monotonically increasing AA x in R , then

Let f(x){{:(max.{absx,x^2}","" "absxle2),(" "8-2absx","" "2ltabsxle4):} .Let S be the set of points in the intercal (-4,4) at which f is not differentible. Then S

If f(x) = {(x - 5, if xle1), (4x^(2) - 9, if (1ltxlt2) , (3x +4, if xge2) :} then the right hand derivative of f(x) at x = 2 is:

A function f (-3 , 7) to R is defined as follows f (x) = {{:( 4 x^(2) + 1 , ,-3 le x lt 2) , (3x - 2 , ,2 le x le 4) , (2x + 3 , ,4 lt x lt 7):}} Find (i) 5 f(1) - 3 f(-2) (ii) 3f (-3) + 4 f (iii) (7 f (3) - f (-1))/(2 f (6) - f(1))

If f(x)={{:((x)/(sinx)",",x gt0),(2-x",",xle0):}andg(x)={{:(x+3",",xlt1),(x^(2)-2x-2",",1lexlt2),(x-5",",xge2):} Then the value of lim_(xrarr0) g(f(x))