Given f ( x ) = x 2 + 4 and g ( x ) = x − 2 .a) Determine (1) ( f ∘ g ) x .b) Domain of f(x)c) Domain of g(x)d) Domain of ( f ∘ g ) x

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Given   f  (  x  )  =      x    2    +  4 and   g  (  x  )  =      x    −    2  .a) Determine (1)  (  f  ∘  g  )  x  .b) Domain of f(x)c) Domain of g(x)d) Domain of   (  f  ∘  g  )  x

abortargy · Accepted Answer

Step 1  f  (  x  )  =      x    2    +  4  ,  g  (  x  )  =      x    −    2  a)   (  f  ∘  g  )  (  x  )  =  f  (  g  (  x  )  )  =  (      x    −    2        )    2    +  4  =  x  −  2  +  4  =  x  +  2b) Domain of   f  (  x  )  ⇒  (  −  ∞  ,  ∞  )c) Domain of   g  (  x  )  ⇒  x  −  2  ≥  0  ,  x  ≥  2  ⇒  [  2  ,  ∞  ]d) Domain of   (  f  ∘  g  )  (  x  )  ⇒  [  2  ,  ∞  ]

Given f(x)=x^2+4 and g(x)=sqrt{x-2}

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