let `f(x)=-x^3+(b^3-b^2+b-1)/(b^2+3b+2)` if `x` is `0` to `1` and `f(x)=2x-3` if `x` if `1` to `3`.All possible real values of `b` such that `f (x)` has the smallest value at `x=1` ,are

Let f(x)={x^3-x^2+10 x-5,xlt=1-2x+(log)_2(b^2-2),x >1 Find the values of b for which f(x) has the greatest value at x=1.

Suppose f(x)={:{(a+bx,x lt 1) ,(4,x=1), (b-ax,x gt 1):} and if lim_(x to 1) f(x)=f(1). What are possible values of a and b?

Let f be a function from R to R defined by f (x) =2x-3 Find the value of a and b given that (a,1) (3,b) belongs to f.

If f(x)= -x^(3)-3x^(2)-2x+a,a in R then the real values of x satisfying f(x^(2)+1)gtf(2x^(2)+2x+3) will be

If A={-3,-2,-1,0,1,2,3} and f : A->B is an onto function defined by f(x)=2x^2+x-2 and find B .

Let f(x)=x+2|x+1|+2|x-1|dot If f(x)=k has exactly one real solution, then the value of k is (a) 3 (b) 0 (c) 1 (d) 2

Let f(x)=x^2-2x-1 AA x in R Let f:(-oo, a]->[b, oo) , where a is the largest real number for which f(x) is bijective. If f : R->R , g(x) = f(x) + 3x-1 , then the least value of function y = g(|x|) is

Let f(x)=a x^2+b x+a ,b ,c in Rdot If f(x) takes real values for real values of x and non-real values for non-real values of x , then a=0 b. b=0 c. c=0 d. nothing can be said about a ,b ,cdot

Statement 1: If 27 a+9b+3c+d=0, then the equation f(x)=4a x^3+3b x^2+2c x+d=0 has at least one real root lying between (0,3)dot Statement 2: If f(x) is continuous in [a,b], derivable in (a , b) such that f(a)=f(b), then there exists at least one point c in (a , b) such that f^(prime)(c)=0.

If 4^x-2^(x+2)+5+||b-1|-3|=|siny|, x , y , b in R , then the possible value of b is_________