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If f (x) = StartFraction x minus 3 Over x EndFraction and g(x) = 5x – 4, what is the domain of (f circle g) (x)?
StartSet x vertical line x not-equals 9 EndSet
StartSet x vertical line x not-equals one-third EndSet
StartSet x vertical line x not-equals four-fifths EndSet
StartSet x vertical line x not-equals 3 EndSet
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sqdancefan

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Answer:

  c.  {x | x ≠ 4/5}

Step-by-step explanation:

Given:

  • f(x) = (x -3)/x
  • g(x) = 5x -4

Find:

  The domain of (f ◦ g)(x)

Solution:

The domain of f(x) excludes the value of x that makes the denominator zero. That is, it is all real numbers except x = 0.

Then the domain of f(g(x)) must exclude any value of x that makes g(x) be zero. That value would be ...

  g(x) = 0 = 5x -4

  4 = 5x . . . . . . . . . . add 4

  4/5 = x . . . . . . . . . .divide by 5

The domain of (f ◦ g)(x) is all real numbers except x = 4/5. In set notation, it could be written ...

  {x | x ≠ 4/5}

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