Let f(x)=x^{2},x\epsilon R. For any A\subseteq R , define 

g(A)={\left \{ x\epsilon R : f(x)\epsilon A}\right \}. If S=[0,4] , then which

one of the following statements is not true ?

  • Option 1)

    g(f(S)) \neq S

  • Option 2)

    f(g(S)) = S

  • Option 3)

    g(f(S)) = g(S)

  • Option 4)

    f(g(S)) \neq f(S)

 

Answers (1)

g(S) = [-2,2]

So, f(g(S)) = [0,4] = S

And f(S) = [0,16] => f(g(S))\neq f(S)

Also,

g(f(S)) = [-4,4] \neq g(S)

So, g(f(S))\neq S

correct option is (3)


Option 1)

g(f(S)) \neq S

Option 2)

f(g(S)) = S

Option 3)

g(f(S)) = g(S)

Option 4)

f(g(S)) \neq f(S)

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