Prove that for real values of `x ,(a x^2+3x-4)//(3x-4^2+a)` may have any value provided a lies between 1 and 7.

Prove that for real values of x ,(a x^2+3x-4)//(3x-4x^2+a) may have any value provided a lies between 1 and 7.

Prove that (6x^(2)-22x+21)/(5x^(2)-18x +17) for real values of x lies between 1 and (5)/(4) .

if for all real value of x,(4x^2+1)/(64x^2-96x.sina+5)<1/32 ,then a lies in the interval

If 7^(log 7(x^(2)-4x + 5))=x - 1 , x may have values

The values of x for which (x-1)/(3x+4) lt (x-3)/(3x-2)

If x be real, prove that the value of (2x^(2)-2x+4)/(x^(2)-4x+3) cannot lie between -7 and 1.

If x is real, prove that the value of the expression ((x-1)(x+3))/((x-2)(x+4)) cannot be between (4)/(9) and 1.

If x is real show sthat the value of (x^(2)+2x+3)/(x^(2)+2x+4) always lies between 2/3 and 1.

If x be real, prove that the value of (11x^(2)+12x+6)/(x^(2)+4x+2) cannot lie between -5 and 3.

Find the values of a for which the expression (ax^2+3x-4)/(3x-4x^2+a) assumes all real values for all real values of x