Consider the quadratic function `f(x)=|m+1|x^2+(m+3)x+1`,`(m!=-1)` then which of the following is/are true? a. f(x)=0 has no real roots for `m in (-5-2sqrt3,-5+2sqrt3)` b. f(x)=0 has no real roots for `m in (-oo,-5-2sqrt3)(-5+2sqrt3,oo)` c. Range of minimum value of f(x) is `(-oo,-1]` d. Range of minimum value of f(x) is `(-oo,-3/4]`

Consider the graph of the function f(x)=e^(I n((x+3)/(x+1))) . Then which of the following is incorrect? (a)domain of f is (-oo,-3)uu(-1,oo) (b) f(x) has no zeroes (c)graph lies completely above the x-axis (d)range of the function is (1,oo)

Consider a real - valued function f(x) = sqrt(sin^(-1) x + 2) + sqrt(1 - sin^(-1)x) The range of f (x) is

Consider a real - valued function f(x) = sqrt(sin^(-1) x + 2) + sqrt(1 - sin^(-1)x) The range of f (x) is

Consider the function f:(-oo,oo)to(-oo,oo) defined by f(x)=(x^2-a)/(x^2+a),a >0, which of the following is not true?(a) maximum value of f is not attained even though f is bounded. (b) f(x) is increasing on (0,oo) and has minimum at x=0 (c) f(x) is decreasing on (-oo,0) and has minimum at x=0. (d) f(x) is increasing on (-oo,oo) and has neither a local maximum nor a local minimum at x=0.

Consider the function f:(-oo,oo)vec(-oo,oo) defined by f(x)=(x^2+a)/(x^2+a),a >0, which of the following is not true? maximum value of f is not attained even though f is bounded. f(x) is increasing on (0,oo) and has minimum at ,=0 f(x) is decreasing on (-oo,0) and has minimum at x=0. f(x) is increasing on (-oo,oo) and has neither a local maximum nor a local minimum at x=0.

Consider the function f:(-oo,oo)vec(-oo,oo) defined by f(x)=(x^2+a)/(x^2+a),a >0, which of the following is not true? maximum value of f is not attained even though f is bounded. f(x) is increasing on (0,oo) and has minimum at ,=0 f(x) is decreasing on (-oo,0) and has minimum at x=0. f(x) is increasing on (-oo,oo) and has neither a local maximum nor a local minimum at x=0.

Consider the function f:(-oo,oo)vec(-oo,oo) defined by f(x)=(x^2+a)/(x^2+a),a >0, which of the following is not true? maximum value of f is not attained even though f is bounded. f(x) is increasing on (0,oo) and has minimum at ,=0 f(x) is decreasing on (-oo,0) and has minimum at x=0. f(x) is increasing on (-oo,oo) and has neither a local maximum nor a local minimum at x=0.

If the range of the function f(x)=3x^(2)+bx+c is [0,oo) then value of (b^(2))/(3c) is

What is the range of the function f(x)=x^(2)+3x-5 in the domain x in[0,oo)?

If f(x)=x^(3)-5x^(2)+5x+1 then value of f(2-sqrt(3)) is