Let `f(x)=a x+ba n dg(x)=c x+d , a!=0.` Assume `a=1,b=2.` If `(fog)(x)=(gof)(x)` for all `x ,` what can you say about `ca n dd ?`

If f(x)=3+x and g(x)=x-4 , show that fog(x)=gof(x)

Let f:R→R:f(x)=x^2 and g: R→R: g(x)=(x+1) . Show that (gof)≠(fog) .

If f(x)=2x+1 and g(x)=x/2 , then find (fog(x))-(gof(x))

Let f(x)=x^2a n dg(x)=sinxfora l lx in Rdot Then the set of all x satisfying (fogogof)(x)=(gogof)(x),w h e r e(fog)(x)=f(g(x)), is +-sqrt(npi),n in {0,1,2, dot} +-sqrt(npi),n in {1,2, dot} pi/2+2npi,n in { ,-2,-1,0,1,2} 2npi,n in { ,-2,-1,0,1,2, }

If f(x)=1+x,g(x)=2x-2 , show that fog=gof

If f(x)=3x-2a n d(gof)^(-1)(x)=x-2, then find the function g(x)dot

Let f be a function such that f(x+y)=f(x)+f(y) for all xa n dya n df(x)=(2x^2+3x)g(x) for all x , where g(x) is continuous and g(0)=3. Then find f^(prime)(x)dot

If f(x)=2x-1,g(x)=(x+1)/2 , show that fog=gof=x

Suppose f(x)=a x+ba n dg(x)=b x+a ,w h e r eaa n db are positive integers. If f(g(20))-g(f(20))=28 , then which of the following is not true? a=15 b. a=6 c. b=14 d. b=3

If f(x)=2x-1, g(x)=(x+1)/(2) , show that fog=gof=x .