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Find the domain of the composite function fog. 1 The domain contains all real numbers except
for which two values? (smaller value) (larger value)
Solution
g(x)=-8/x
domain of g does not contain 0
fog
=f(g(x))
=1/((-8/x)+9)
=1/((-8+9x)/x)
=x/(9x -8)
function is undefined if 9x -8=0
=>x =8/9
so domain is all real numbers except 0, 8/9

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  • 1. Find the domain of the composite function fog. 1 The domain contains all real numbers except for which two values? (smaller value) (larger value) Solution g(x)=-8/x domain of g does not contain 0 fog =f(g(x)) =1/((-8/x)+9) =1/((-8+9x)/x) =x/(9x -8) function is undefined if 9x -8=0 =>x =8/9 so domain is all real numbers except 0, 8/9