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

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

If f(x)=(a x^2+b)^3, then find the function g such that f(g(x))=g(f(x))dot

If the functions f and g defined from the set of real number R to R such that f(x) = e^(x) and g(x) = 3x - 2, then find functions fog and gof. Also, find the domain of the functions (fog)^(-1) and (gof)^(-1) .

If f,g and h are differentiable functions of x and Delta = |{:(f , g , h), ((xf)' , (xg)' , (xh)'), ((x^(2) f)'' , (x^(2) g)'', (x^(2) h)''):}| then prove that Delta'=|{:(f , g , h), (f' , g' , h'), ((x^(3) f'')' , (x^(3) g'')', (x^(3) h)'')':}| .

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) .

If the functions f, g and h are defined from the set of real numbers R to R such that f(x)=x^(2)-1,g(x)=sqrt((x^(2)+1)) , h(x)={{:("0,","if",xle0),("x,","if",xge0):} Then find the composite function hofog and determine whether the function fog is invertible and h is the identity function.

Let f : R rarr R be defined as f(x) = 10 x +7 . Find the function g:R rarrR such that gof = fog = I_(g)

Let f,g, h be differentiable functions of x. if Delta = |(f,g,h),((xf)',(xg)',(xh)'),((x^(2) f)'',(x^(2)g)'',(x^(2) h)'')|and, Delta' = |(f,g,h),(f',g',h'),((x^(n)f'')',(x^(n) g'')',(x^(n) h'')')| , then n =