Let `f(x)=x^2` and `g(x)=2^x` . Then the solution set of the equation `fog(x)=gof(x)` is `(a)R` (b) {0} (c) {0, 2} (d) none of these

Let f(x)=x^2+x+1 and g(x)=sinx . Show that fog!=gof .

The number of solution of equation |x-1|=e^x is (A) 0 (B) 1 (C) 2 (D) none of these

The number of solution of equation |x-1|= e^x is (A) 0 (B) 1 (C) 2 (D) none of these

The number of real solutions of the equation e^(|x|)-|x|=0 , is A. o B. 1 c. 2 D. None of these.

If f(x)=sqrt(x+3) and g(x)=x^2+1 be two real functions, then find fog and gof .

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 (a) +-sqrt(npi),n in {0,1,2, dot} (b) +-sqrt(npi),n in {1,2, dot} (c) pi/2+2npi,n in { ,-2,-1,0,1,2} (d) 2npi,n in { ,-2,-1,0,1,2, }

Let f(x)=[x] and g(x)=|x| . Find (gof)(5/3) fog(5/3)

Let f(x)=[x] and g(x)=|x| . Find (gof)(5/3) fog(5/3)

If g(x)=x^2+x-2a n d1/2gof(x)=2x^2-5x+2, then which is not a possible f(x)? (a)2x-3 (b) -2x+2 (c) x-3 (d) None of these

If g(x)=x^2+x-2a n d1/2gof(x)=2x^2-5x+2, then which is not a possible f(x)? (a) 2x-3 (b) -2x+2 (c) x-3 (d) None of these