Let f, g and h be functions from R to R. Show that
`(f +g ) oh = foh+ goh`
`(f. g) oh = ( foh). (goh)`

Let f : R rarr R be any function. Define g : R rarr R by g(x)=|f(x)| for all x. Then g is:

Let f : R to R be defined as f (x) =10 x +7. Find the function g : R to R such that g o f =f 0 g= 1 _(R).

Let the function f : R to R , g : R to R , h : R to R be defined by f(x) = cos x,g(x) = 2x+1 and h(x) = x^(3)-x-6 , Find the mapping h o (go h) , hence find the value of h o (go f), hence find the value of ( h o (go f) ) (x) when x=(pi)/(3) and c=(2pi)/(3).

Let f and g be continuous fuctions on [0, a] such that f(x)=f(a-x)" and "g(x)+g(a-x)=4 " then " int_(0)^(a)f(x)g(x)dx is equal to

Let the function f:R to R be defined by f(x)=x+sinx for all x in R. Then f is -

Let f(x)=x^2 and g(x)=sinx for all xIR then the set of all x satisfying (f o g o g o f ), (x)=(g o g o f) , (x) , where (f o g ) , (x)=f(g(x)) , is

Let f, g and h are differentiable functions. If f(0) = 1; g(0) = 2; h(0) = 3 and the derivatives of theirpair wise products at x=0 are (fg)'(0)=6;(g h)' (0) = 4 and (h f)' (0)=5 then compute the value of (fgh)'(0) .

Give examples of two functions f : N to N and g : N to N such g o f is onto but f is not onto.

Let f:R to R where f(x) =sin x. Show that f is into. Also find the codomain if f is onto.

Let R be the set of real numbers . If the function f : R to R and g : R to R be defined by f(x) = 4x+1 and g(x)=x^(2)+3, then find (go f ) and (fo g) .