Determine the sign of the function `3x^(2)-2x+1` for real values of x.

Find the sign of 6x^(2)-5x+1 for all real value of x.

Determine the sign of the expression i) x^(2)+x+1 ii) -x^(2)+x-1 for x in R .

consider the function f(X) = 3x^(4)+4x^(3)-12x^(2) The range of values of a for which f(x) = a has no real

A function f is defined on the set of real numbers as follows: f(x)={(x+1, 1 le x lt 2),(2x-1, 2 le x lt 4), (3x-10, 4 le x lt 6):} (a) Find the domain of the function. (b) Find the range of the function.

Q. f={ (x+a if x =0) g(x)={(x+1 if x =0) where a and b are non-negative real numbers. Determine the composite function gof . If (gof)(x) is continuous for all real x, determine the values of a and b, Further for these values of a and b, is gof differentiable at x=0? Justify your answer.

Find the values ' a ' for which the function f(x)=(a+2)x^3-3a x^2+9a x-1 decreases for all real values of x .

If the equation 2^(2x)+a*2^(x+1)+a+1=0 has roots of opposite sign, then the exhaustive set of real values of a is (a)(−∞,0) (b)(−1,−2/3) (c)(−∞,−2/3) (d)(−1,∞)

Determine the value of the constant k so that the function f(x)={k x^2,\ \ \ if\ xlt=2 3,\ \ \ if\ x >2 is continuous at x=2 .

Find the domain of each of the following real valued functions of real variable: f(x)=(3x-2)/(x+1)

Find the values of a for which the function f(x)=(a+2)x^3-3a x^2+9a x-1 decreasing for all real values of xdot