Find the values of a and b if `f(x)={a+sin^(-1)(x+b), xgeq1 and x ,x<1` is differentiable at `x=1.`

find the values of a and b , such that f(x) ={ax^2+1,xle1 and x^2+ax+b , x gt1 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 a and b , if the function f(x) defined by f(x)={x^2+3x+a ,\ \ xlt=1b x+2,\ \ \ \ \ \ \ \ \ \ x >1 is differentiable at x=1 .

Find the value of a ,b if f(x) = {((a e^(1//|x+2|) - 1)/(2-e^(1//|x+2|)),; -3 lt x lt -2), (b,; x = -2), (sin((x^4-16)/(x^5+32)),; -2 lt x lt 0):} is continuous at x = -2.

Find the values of a and b , if the function f defined by f(x)={x^2+3x+a ; if xlt=1, b x+2 ; if x >1 is differentiable at x=1

Let f(x)={x^3-x^2+10 x-5,xlt=1, \ -2x+(log)_2(b^2-2),x >1 Find the values of b for which f(x) has the greatest value at x=1.

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)

Let f(x) =e^(x-1)-ax^(2)+b and g(x)={{:(e^(x-1),xle1),(x^(2)+1,xgt1):}, then find the values of a and b such that f(x) xx g(x) is differentiable at x=1 .

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