Maths-
General
Easy

Question

Let f left parenthesis x right parenthesis equals sin space x text  and  end text g left parenthesis x right parenthesis equals log invisible function application vertical line x vertical line

  1. R subscript 1 equals left curly bracket u colon negative 1 less or equal than u less or equal than 1 right curly bracket comma R subscript 2 equals left curly bracket v colon negative straight infinity less than v less than 0 right curly bracket
  2. R subscript 1 equals left curly bracket u colon negative straight infinity less than u less or equal than 0 right curly bracket comma R subscript 2 equals left curly bracket v colon negative 1 less or equal than v less or equal than 1
  3. R subscript 1 equals left curly bracket u colon negative 1 less than u less than 1 right curly bracket comma R subscript 2 equals left curly bracket v colon negative straight infinity less than v less than 0 right curly bracket
  4. R subscript 1 equals left curly bracket u colon negative 1 less or equal than u less or equal than 1 right curly bracket comma R subscript 2 equals left curly bracket v colon negative straight infinity less than v less or equal than 0 right curly bracket

hintHint:

The composition of functions f(x) and g(x) where g(x) is acting first is represented by f(g(x)) or (f ∘ g)(x). It combines two or more functions to result in another function. In the composition of functions, the output of one function that is inside the parenthesis becomes the input of the outside function. i.e.,
  • In f(g(x)), g(x) is the input of f(x).
  • In g(f(x)), f(x) is the input of g(x).

The correct answer is: R subscript 1 equals left curly bracket u colon negative 1 less or equal than u less or equal than 1 right curly bracket comma R subscript 2 equals left curly bracket v colon negative straight infinity less than v less or equal than 0 right curly bracket


    G i v e n space colon space f left parenthesis x right parenthesis equals sin space x text  and  end text g left parenthesis x right parenthesis equals log vertical line x vertical line
    Now, we have (fog)(x) = f (g(x))
    rightwards double arrowf(log open vertical bar x close vertical bar) = sin(log open vertical bar x close vertical bar)
    Thus, R1 = open curly brackets u space colon space minus 1 space less or equal than space u space less or equal than open 1 close curly brackets close
    Also, (gof) = g (f(x)) = g(sinx) = log open vertical bar sin left parenthesis x right parenthesis close vertical bar
    Since, 0 less or equal than space open vertical bar sin space left parenthesis x right parenthesis close vertical bar comma space less or equal than space 1 comma space w e space g e t comma
    R2 = Error converting from MathML to accessible text.
    Thus, Error converting from MathML to accessible text.

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