f(x)=^(16-x)C_(2x-1)+^(20-3x)P_(4x-5)

Range of f(x)=.^(16-x)C_(2x-1)+^(20-3x)C_(4x-5)

The domain of defination of the function ""^(16-x)C_(2x-1) +""^(20-3x)P _(4x-5) is-

Domain of function f(x)=log_([x+(1)/(x)])|x^(2)-x-6|+^(16-x)C_(2x-1)+^(20-3x)P_(2x)

(16x^(2)-20x+9)/(8x^(2)+12x+21)=(4x-5)/(2x+3)

Find the intervals in which the following function are increasing or decreasing. f(x)=10-6x-2x^2 f(x)=x^2+2x-5 f(x)=6-9x-x^2 f(x)=2x^3-12 x^2+18 x+15 f(x)=5+36 x+3x^2-2x^3 f(x)=8+36 x+3x^2-2x^3 f(x)=5x^3-15 x^2-120 x+3 f(x)=x^3-6x^2-36 x+2 f(x)=2x^3-15 x^2+36 x+1 f(x)=2x^3+9x^2+20 f(x)=2x^3-9x^2+12 x-5 f(x)=6+12 x+3x^2-2x^3 f(x)=2x^3-24 x+107 f(x)=-2x^3-9x^2-12 x+1 f(x)=(x-1)(x-2)^2 f(x)=x^3-12 x^2+36 x+17 f(x)=2x^3-24+7 f(x)=3/(10)x^4-4/5x^3-3x^2+(36)/5x+11 f(x)=x^4-4x f(x)=(x^4)/4+2/3x^3-5/2x^2-6x+7 f(x)=x^4-4x^3+4x^2+15 f(x)=5x^(3/2)-3x^(5/2),x >0 f(x)==x^8+6x^2 f(x)==x^3-6x^2+9x+15 f(x)={x(x-2)}^2 f(x)=3x^4-4x^3-12 x^2+5 f(x)=3/2x^4-4x^3-45 x^2+51 f(x)=log(2+x)-(2x)/(2+x),xR

Use the Factor Theorem to determine whether g(x) is factor of f(x) in each of the following cases : (i) f(x)=5x^(3)+x^(2)-5x-1, g(x)=x+1 (ii) f(x)=x^(3)+3x^(2)+3x+1,g(x)=x+1 (iii) f(x)=x^(3)-4x^(2)+x+6,g(x)=x-2 (iv) f(x)=3cx^(3)+x^(2)-20x+12,g(x)=3x-2 f(x)=4x^(3)+20x^(2)+33x+18,g(x)=2x+3

If int((2x-8)/((x-1)(x-3)(x-5)(x-7)+16))dx=lambda-(1)/(f(x)) Where f(x) is of the form of ax^(2)+bx+c , then

Let f(x)+f(y)=f(x sqrt(1-y^(2))+y sqrt(1-x^(2)))[f(x) is not identically zerol.Then f(4x^(3)-3x)+3f(x)=0f(4x^(3)-3x)=3f(x)f(2x sqrt(1-x^(2))+2f(x)=0f(2x sqrt(1-x^(2))=2f(x)

Show that (2x + 1) is a factor of the expression f(x) = 32x^(5) - 16x^(4) + 8x^(3) + 4x + 5 .