Determine f(x), when `f(x+3)=2x^(2)-3x-1`.

Determine for which cases of the followings the polynomial g(x) will be a factor of f(x). When f(x)=3x^(3)+x^(2)-20x+12andg(x)=3x-2 ,

If f(x+1)=2x^(2)-3x-1 , then f(0) =

The value of c in Rolle's theorem when f(x)=2x^(3)-5x^(2)-4x+3, x in [(1)/(2),3] is -

If f(x)=2^x the f(x+3)/ f(x-1) =?

If the polynomial f(x) be defined by f(x) = {{:(2x^(2)-3 " when " xle2),(2x+1 " when "2ltxle4),(1/(2x-1) "when "xgt4):} then find (a)f(sqrt2),(b)f(pi) .

Let {:(f(x)=5x-4," ""when "0ltxle1),(=4x^(2)-3x," ""when "xgt1):} Discuss the differentiability of f(x) at x = 1 .

If f, RR to RR is defined by f (x) ={{:((x-2)/(x ^(2) -3x+2)"," ,"when " x in RR-{1","2}),(2",","when" x=1),(1",", "when" x=2):} then lim _(xto2) (f(x) -f(2))/(x-2) is equal to-

A function f (x) is defined as follows : f(x)={{:(2-x",","when "xlt1),(x^(2)-3x",","when "xge1):} Examine the differentiability of the function f (x) at x= 1 , hence state whether f (x) is continuous at x = 1 or not .

Use the Factor Theorem to determine whether g (x) is factor of f(x) in each of the following cases: (i) f (x) = 5x ^(3) + x ^(2)-5x -1, g (x)=x +1 (ii) f (x) = x ^(3) + 3x ^(2) + 3x +1 , g(x) =x +1 (iii) f (x) =x ^(3) - 4x ^(2) +x + 6, g (x) =x -2 (iv) f (x) = 3x ^(3) - 20x + 12, g (x) = 3x -2 (v) f (x) = 4x ^(3) + 20 x ^(2) + 33 x +18, g (x) =2x +3

Draw the graph of the function : f(x)=1+2x," when "xle1 =3-x," when "x gt1 From the graph examine whether f(x) is continuous at x = 1 or not.