Find the values of `aa n db` if `f(x)={a+sin^(-1)(x+b),xgeq1x ,x<1` is differentiable at `x=1.`

Find the values of aandb if f(x)={a+sin^(-1)(x+b),x>=1 and x,x< is differentiable at x=1

Find the value of x for which f(x) = 2 sin^(-1) sqrt(1 - x) + sin^(-1) (2 sqrt(x - x^(2))) is constant

Find the values of aa n db so that the function f(x) defined by f(x)={x^2+a x+b,0lt=x<2 3x+2,2lt=xlt=42a x+5b ,4

Find the values of aa n db so that the function f(x)={x^2+3x+a ,ifxlt=1b x+2,ifx >1 is differentiable at each x in Rdot

ind the value of a and b if f(x) is continuous at x=0. If f(x)={(sin(a+1)x+2sin x)/(2),x 0}

Find the inverse of the function: f(x)={x^3-1, ,x<2x^2+3,xgeq2

find the maximum value of f(x) = (sin^(-1) (sin x))^(2) - sin^(-1) (sin x)

If f(x)={x ,\ xlt=1x^2+b x+c ,\ x >1 , then find the values of b\ a n d\ c if f(x) differentiability at x=1.

Find the values of k for which |(x^(2)+kx+1)/(x^(2)+x+1)|<2,AA x in R

For which values of x, function f(x) = sin^(-1) x + sin^(-1).(1)/(x) + cos^(-1) x + cos^(-1).(1)/(x) is defined? Also, find the range