Find the following f ( x ) = x 2 − 16 , g ( x ) = x 2 x 2 + 1 a ) ( f + g ) ( x ) = b ) ( f − g ) ( x ) = c ) ( f g ) ( x ) = d ) ( f / g ) ( x ) =What is the domain of f/g?

Question

Find the following  f  (  x  )  =            x      2        −    16    ,        g  (  x  )  =            x      2                      x        2            +      1        a  )  (  f  +  g  )  (  x  )  =    b  )  (  f  −  g  )  (  x  )  =    c  )  (  f  g  )  (  x  )  =    d  )  (  f      /    g  )  (  x  )  =What is the domain of f/g?

neobuzdanio · Accepted Answer

f  (  x  )  =            x      2        −    16    ,        g  (  x  )  =            x      2                      x        2            +      1          a  )  (  f  +  g  )  (  x  )  =  f  (  x  )  +  g  (  x  )    =            x      2        −    16    +            x      2                      x        2            +      1          b  )  (  f  −  g  )  (  x  )  =  f  (  x  )  −  g  (  x  )    =            x      2        −    16    −            x      2                      x        +            1          c  )  (  f  g  )  (  x  )  =  f  (  x  )  ⋅  g  (  x  )    =            x      2        −    16              x      2              (              x        2            +      1      )          =                    x        2                              x          2                −        16                            x        2            +      1          d  )  (  f      /    g  )  (  x  )  =            f      (      x      )              g      (      x      )          =                    x        2            −      16              x              (                  x          2                +        1        )              =                              x          2                −        16            (              x        2            +      1      )              x      2      For domain of (f/g)(x)      x    2    ≠  0  ⇒  x  ≠  0 (i)and      x    2    −  16  ≥  0    ⇒  (  x  +  4  )  (  x  −  4  )  ≥  0    ⇒  x  ∈  (  −  ∞  ,  −  4  ]  ,  [  4  ,  ∞  )  (ii)From (i) and (ii)Domain of   f      /    g  ⇒  (  −  ∞  ,  −  4  ]  ,  [  4  ,  ∞  )

Find the following f(x)=sqrt(x^2-16) g(x)=(x^2)/(x^2+1) a) (f+g)(x)= b) (f-g)(x)= c) (fg)(x)= d) (f/g)(x)= What is the domain of f/g?

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