Let `f(x)={(4x-5,xge2),(1-x,x<2):}` and `g(x)={(3x+7,xle3),(7,x>3):}` be two functions from R to R. Find `(fog)(7)`

Let f(x)={(4x-5,xge2),(1-x,x 3):} be two functions from R to R. Find (fog)(3)

Let f(x)={(4x-5,xge2),(1-x,x 3):} be two functions from R to R. Find (gof)(1)

Let f(x)={(4x-5,xge2),(1-x,x 3):} be two functions from R to R. Find (gof)(10)

Let f{(x,(x^2)/(1+x^2):x in R} be a function from R into R.Determine the range of f.

Let f:R toR and g:R to R be two functions given by f(x)=cosx and g(x)=3x^(2) . Show that gof!=fog .

Let f : R rarr R, f(x)=x^2 and g : R rarr R,g(x)=sinx be two given functions. Is gof=fog ?

If f(x) = x + 7 , and g(x)=x-7 , x in R. Find (f0g)(7)?

Show that f(x)=e^(1//x) is a strictly decreasing function for all x in R .

Let f:R to R and g: R to R be two functions defined by f(x)=|x|" and "g(x)=[x] , where [x] denotes the greatest integer less than or equal to x. Find (fog) (5.75) and (gof)(-sqrt(5)) .