If f:R->R,f(x)=x-2,g:R->R,g(x)=x+2 then (f+g)(x) =_______ (A)x (B) x2-4 (C) 2x (D)4​

Question

If f:R->R,f(x)=x-2,g:R->R,g(x)=x+2 then (f+g)(x) =_______
(A)x (B) x2-4 (C) 2x (D)4​

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Jasmine 3 months 2021-11-02T17:05:06+00:00 1 Answer 0 views 0

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    2021-11-02T17:07:05+00:00

    The function \displaystyle\sf {f:\mathbb{R}\to\mathbb {R}} is defined as,

    \displaystyle\longrightarrow\sf{f(x)=x-2}

    The function \displaystyle\sf {g:\mathbb{R}\to\mathbb {R}} is defined as,

    \displaystyle\longrightarrow\sf{g(x)=x+2}

    Then,

    \displaystyle\longrightarrow\sf{(f+g)(x)=f(x)+g(x)}

    \displaystyle\longrightarrow\sf{(f+g)(x)=x-2+x+2}

    \displaystyle\longrightarrow\underline {\underline {\sf{(f+g)(x)=2x}}}

    Hence (C) is the answer.

    Additional Information:-

    For two real functions \displaystyle\sf {f(x)} and \displaystyle\sf {g(x),}

    • \displaystyle\sf {(f+g)(x)=f(x)+g(x)}
    • \displaystyle\sf {(f-g)(x)=f(x)-g(x)}
    • \displaystyle\sf {(fg)(x)=f(x)\cdot g(x)}
    • \displaystyle\sf {\left(\dfrac {f}{g}\right) (x)=\dfrac {f(x)}{g(x)},\ g(x)\neq 0}

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