Let `f(x)={x^2; xgeq0a x ; x<0` Find real values of a such that `f(x)` is strictly monotonically increasing at `x=0`

Let f(x) = {-x^2 ,for x<0; x^2+8 ,for xgeq0 Find x intercept of the common tangent to f(x) .

Let f(x)={x^2-4x+3, ,x<3; x-4,xgeq3 a n d g(x)={x-3,x<4; x^2+2x+2,xgeq4 Describe the function f/g and find its domain.

Let f(x)={x^2-4x+3, ,x<3; x-4,xgeq3 a n d g(x)={x-3,x<4; x^2+2x+2,xgeq4 Describe the function f/g and find its domain.

If f(x)={x^2, for xgeq1 ; x for x<0 ,then fof(x) is given by

f(x)=x+1, x<0, f(x)=x^2, xgeq0 and g(x)={x^3, x<1, 2x-1, xgeq1 Then find f(g(x)) and find its domain and range.

Let f(x)={cos[x],xgeq0|x|+a ,x 0) f(x) exists, where [x] denotes the greatest integer function less than or equal to x .

Let f(x)={x^3+x^2+10 x ,\ \ x<0-3sinx ,\ \ \ \ xgeq0 . Investigate x=0 for local maxima/minima.

If f(x)={x^2, for xgeq1x ,for x<0 ,t h e n fof(x) is given by

If f(x)=x^2 for xgeq1 and x for x<0 ,then fof(x) is given by

Let f(x)=(x+1)^2-1, xgeq-1. Then the set {x :f(x)=f^(-1)(x)} is {0,1,(-3+isqrt(3))/2,(-3-isqrt(3))/2} (b) {0,1,-1 {0,1,1} (d) e m p t y