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

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

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

Find the value of the constant k so that the given function is continuous at the indicated point: f(x)={k x^2,\ \ \ xgeq1 4,\ \ \ x<1 at x=1

Suppose f(x)=(x+1)^2forxgeq-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-sqrt(x)-1,xgeq0 (b) 1/((x+1)^2),x >-1 sqrt(x+1,)xgeq-1 (d) sqrt(x)-1,xgeq0

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

If f(x)={x-1,xgeq 1 2x^2-2,x 0-x^2+1,xlt=0,a n dh(x) =|x|,t h e n lim_(x->0)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 values of a and b if f(x)={a+sin^(-1)(x+b), xgeq1 and x ,x<1 is differentiable at x=1.

f(x)={x+1, x<0,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),xgeq0, be a non-negative continuous function, and let f(x)=int_0^xf(t)dt ,xgeq0, if for some c >0,f(x)lt=cF(x) for all xgeq0, then show that f(x)=0 for all xgeq0.