`{x in IR :(2x-1)/(x^3+4x^2+3x) in IR}=`

{x in RR:(2x-1)/(x^(3)+4x^(2)+3x) in RR}=

{x in IR : cos 2x + 2 cos^(2) x - 2 = 0}=

Check whether the following are quadratic equation (i) (x+1)^2=2(x-3) (ii) x^2-2x=(-2)(3-x) (iii) (x-2)(x+1)=(x-1)(x+3) (iv) (x-3)(2x+1)=x(x+5) (v) (2x-1)(x-3)=(x+5)(x-1) (vi) x^2+3x+1=(x-2)^2 (vii) (x+2)^3=2x(x^2-1) (viii) x^3-– 4x^2 – x + 1 = (x – 2)^3

Solve the following equations where x in R a) (x-1)|x^(2)-4x+3|+2x^(2)+3x-5=0 b) |x^(2)+4x+3|+2x+=0 c) |x+3|(x+1)+|2x+5|=0

Solve the following equations where x in R a) (x-1)|x^(2)-4x+3|+2x^(2)+3x-5=0 b) |x^(2)+4x+3|+2x+=0 c) |x+3|(x+1)+|2x+5|=0

Let A = IR- {3}, B = IR - {1} and let f: A to B be defined by f(x) = ( x- 2)/(x - 3) .Then which of the following is not true?

Let f(x) = (1-x)^(2) sin^(2)x+ x^(2) for all x in IR and let g(x) = int_(1)^(x)((2(t-1))/(t+1)-lnt) f(t) dt for all x in (1,oo) . Consider the statements : P : There exists some x in IR such that f(x) + 2x = 2 (1+x^(2)) Q : There exist some x in IR such that 2f(x) + 1 = 2x(1+x) Then

A function f: IR ->IR , where IR , is the set of real numbers, is defined by f(x) = (ax^2 + 6x - 8)/(a+6x-8x^2) Find the interval of values of a for which is onto. Is the functions one-to-one for a =3 ? Justify your answer.