Let `f(x)=x+1/xa n dg(x)=(x+1)/(x+2)` Match the composite function given in Column I with respective domains given in Column II Column I, Column II `fog(x)` , p. `R-{-2,-5/3}` `gof(x)` , q. `R-{-1,0}` `fof(x)` , r. `R-{0}` `gog(x)` , s. `R-{-2,-1}` , t `R-(-1}`

f(x) = |x-1|, f: R^+->R, g(x) = e^x, g:[-1,oo)->R . If the function fog(x) is defined, then it domain and range respectively are:

Match the statements/expression given in Column I with the values given in Column II. Column I, Column II (p) The number of polynomials f(x) with non-negative integer coefficients of degree lt=2, satisfying f(0)=0 and int_0^1f(x)dx=1,i s , 8 (q) The number of points in the interval [-sqrt(13),sqrt(13)] at which f(x)=sin(x^2)+"cos"(x^2) attains its maximum value, is, 2 (r) int_(-2)^2(3x^2)/(1+e^x)dx equals, 4 (s)(int_(-2)^2cos2xdotlog((1+x)/(1-x))dx)/(int_0^ (1/2)""cos2xdotlog((1+x)/(1-x))dx) , 0

Let f: R ->R be defined as f(x) = 10 x + 7 . Find the function g: R ->R such that gof=fog=I_R

Let A=(x in R: x ge 1) . The inverse of the function of f:A to A given by f(x)=2^(x^((x-1)) . Is

Show that the function f: R-{3}->R-{1} given by f(x)=(x-2)/(x-3) is bijection.

Let f(x)=sinx and g(x)=(log)_e|x| If the ranges of the composition functions fog and gof are R_1 and R_2, respectively then (a) R_1{u:-1 le u < 1}, R_2={v:-oo v < 0} (b) R_1={u:-oo < u < 0}, R_2={v:-oo < v < 0} (c) R_1={u:-1 < u < 1},R_1={v:-oo V le 0}

Show that the function f: R-{3}->R-{1} given by f(x)=(x-2)/(x-3) is a bijection.

If the function f: R->R be given by f(x)=x^2+2 and g: R->R be given by g(x)=x/(x-1) . Find fog and gof .

If f : R to R , f (x) =x ^(3) and g: R to R , g (x) = 2x ^(2) +1, and R is the set of real numbers then find fog(x) and gof (x).

Consider the function f:R -{1} to R -{2} given by f {x} =(2x)/(x-1). Then