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

: If f(x)={x^2+2,xgeq2 1-x ,x 1, 3-x , xlt=0,t h e nt h ev a l u eoflim_(x->1)f(g(x))i s__

Suppose f(x)=(x+1)^2 for xgeq-1. If g(x) is the function whose graph is the reflection of the graph of f(x) with respect to the line y=x , then g(x) equal. (a) 1-sqrt(x-1),xgeq0 (b) 1/((x+1)^2),x gt-1 (c) sqrt(x+1,)xgeq-1 (d) sqrt(x)-1,xgeq0

If f(x)={x-1,xgeq1 2x^2-2,x 0-x^2+1, xlt=0,and h(x)=|x| ,t h e n("lim")_(xvec0)f(g(h(x))) is___

If f(x)=|[x-2, (x-1)^2, x^3] , [(x-1), x^2, (x+1)^3] , [x,(x+1)^2, (x+2)^3]| then coefficient of x in f(x) is

Find lim_(x to 1) f(x) if f(x)={:{(x^2-1,x le1),(x^2+1, x gt1):}

If f(x)=x^(3/2)(3x-10),xgeq0, then f(x) is increasing in ____.

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

Let f:[1,oo] be a differentiable function such that f(1)=2. If 6int_1^xf(t)dt=3xf(x)-x^3 for all xgeq1, then the value of f(2) is

Which of the following function has point of extremum at x=0? f(x)=e^(-|x|) f(x)="sin"|x| f(x)={x^2+4x+3,x<0-x , xgeq0 f(x)={|x|,x<0{x},0lt=x<1 (where {x} represents fractional part function).