Find number of roots of f(x) where `f(x) = 1/(x+1)^3 -3x + sin x`

Find k if fog=gof where f(x)=3x-1 , g(x)=4x+k .

Find f'(x) if f(x) = cos^(-1) ( 4x^3 - 3x) .

Find the approximate value of f(3.02) where f(x) =3x^(2) + 5x + 3 .

The number of points in R in which the function f(x) = |x - 1| + | x- 3 | + sin x is not differentiable is …………… .

Find the relation between a and b if lim_(x to 3) f(x) exists where f(x) ={ {:( ax+b , "if " x gt 3),(3ax - 4b +1 , "if " x lt 3):}

Find lim_(x rarr 3)f(x),where f(x)=[|x-3|]/[x-3] ,xne3 .

For each of the functions find the f _(x), f _(y), and show that f _(xy) = f _(yx). f (x,y) = (3x)/( y + sin x)