Let `f(x)` be defined on `[-2,2]` and be given by `f(x)`=`{−1;−2≤x≤0}` and`f(x)`=`{x−1`;`0`<`x`≤`2`}` ​ . and `g(x)=`f(|x|)+|f(x)|` Find g(x)

Let f(x) be defined on [-2,2] and be given by f(x)={(-1",",-2 le x le 0),(x-1",",0 lt x le 2):} and g(x)=f(|x|) +|f(x)| . Then find g(x) .

If f(x) is defined on [0,1], then the domain of f(3x^(2)) , is

Let f:N->N be defined by f(x)=x^2+x+1,x in N . Then f(x) is

Let f be a function defined on [0,2]. Then find the domain of function g(x)=f(9x^2-1)

Let g(x) be a polynomial of degree one and f(x) is defined by f(x)={g(x) , xleq0 and ((1+x)/(2+x))^(1/x) , xgt0 } Find g(x) such that f(x) is continuous and f'(1)=f(-1)

Let f(x) be the function given by f(x)=arc cos ((1-x^(2))/(1+x^(2))).Then

Let f (x) be function defined on [0,1] such that f (1)=0 and for any a in (0,1], int _(0)^(a) f (x) dx - int _(a)^(1) f (x) dx =2 f (a) +3a +b where b is constant. The length of the subtangent of the curve y= f (x ) at x=1//2 is:

Let f (x) be a conitnuous function defined on [0,a] such that f(a-x)=f(x)"for all" x in [ 0,a] . If int_(0)^(a//2) f(x) dx=alpha, then int _(0)^(a) f(x) dx is equal to

Let f(x) be defined as f(x)={tan^(-1)alpha-5x^2,0ltxlt1 and -6x ,xgeq1 if f(x) has a maximum at x=1, then find the values of alpha .

Let f defined on [0, 1] be twice differentiable such that |f " (x)| <=1 for x in [0,1] ,if f(0)=f(1) then show that |f'(x)|<1 for all x in [0,1] .