[" (3).Supposs "f(x)={[a+bx,x<1],[4,x=1]],[" and if "lim_(x rarr1)f(x)=f(1)" .Fhen what are the "],[" porsible value of a "4" b? "]

f(x)=[[a+bx,,x 1

Let f:R rarr R be a continuous odd function,which vanishes exactly at one point and f(1)=(1)/(2). supposs that F(x)=int_(-1)^(x)f(t)dt for all x in[-1,2] and G(x)=int_(-1)^(x)t|f(f(t))|dt for all x in[-1,2]. If lim_(x rarr1)(F(x))/(G(x)) Then the value of f((1)/(2)) is

Let a and b be constants f(x) = a sin x + bx cos x + 2x^2 If f(3) = 15, then f(-3) is

A function f (x) is defined as f(x)={{:(ax+2,"when "xle3),(bx+3,"when " xgt3):} If f (x) is continuous at x =3 then find the relation between a and b .

Suppose f(x)={(a+bx, x 1):} and if lim_(xto1) f(x)=f(1), what are the values of a and b?

Suppose f(x)={(a+bx, x 1):} and if lim_(xto1) f(x)=f(1) , what are the values of a and b?

Find the relation between 'a' and 'b' if the function f defined by f(x)={(ax+1,xle3),(bx+3,x>3):} is continuous.

If f(x) is continuous at x=3 , where f(x)={:(ax+1", for " x le 3),(bx+3", for " x gt 3):} , then

(i) If y = f(x) = (3x-1)/(5x-3) , prove that f(y) = x (ii) If y = f(x) = (ax -b)/(bx-a) , prove that f(y) = x

Determine the values of a,b,c for which the function f(x)={(sin(a+1)x+sin x)/(x),quad f or x<0c,quad f or x=0(sqrt(x+bx^(2)))/(bx^(3/2)),quad f or x is continuous at x=0