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# Functions

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Let f(x) = 1/(x - 8).  Find the largest x that is not in the domain of g(x) = f(f(x)).

Jun 11, 2021

#1
+288
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Let f(x) = 1/(x - 8).  Find the largest x that is not in the domain of g(x) = f(f(x)).

Key idea:    Rational function : The denominator cannot be zero, any x value that makes denominator equal zero is not in the domain.

$$f(f(x)) = \frac{1}{(\frac {1} {x-8}) -8}$$

$$g(x) = \frac{1}{\frac{65-8x}{x-8}}$$

$$g(x) = \frac{x-8}{65-8x}$$

If (65 -8x = 0) that x value is not the domain of g(x)

65-8x = 0

x = (65/8) = 8.125    the largest x that is not in the domain of g(x)

Jun 11, 2021