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

Suppose f(x)=(x+1)^2 forxgeq-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,a n dh(x) =|x|,t h e n("lim")_(xvec0)f(g(h(x))) is___

If f(x)={:{(x^2", "x le 1),( x^2-x+1"," x gt1):} then show that f(x) is not differentiable at x=1 .

Find the points of discontinuity, if any, of the following function: f(x)={-2 , if xlt=-1 2x , if-1

Find the equation of tangent and normal to the curve f(x)={x-2 if x<1x^2-x-1 if xgeq1 a t x=1 if it exists

If f(x)=(x-1)/(2x^(2)-7x+5) for x!=1 and f(x)=-(1)/(3) for x=1 then f'(1)=

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).

If f(x)=x for 0<=x<(1)/(2),f(x)=1f or x=(1)/(2) and f(x)=1- for (1)/(2)<<1 then at x=(1)/(2) the function is

If f(x)=1+x+x^(2)+..... for |x|lt1 then show that f^(-1)(x)=(x-1)/(x)