document.write( "Question 1205646: If f(x) = log x - 4 and g(x) = $\"1%2F%28x%2B4%29\"$ , for what value(s) of x is g(f(x)) undefined? Explain by making reference to the algebraic properties (do not graph). \n" ); document.write( "

Algebra.Com's Answer #842584 by math_tutor2020(3817) $\"\"$ $\"About$

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\n" ); document.write( "Assuming $\"f%28x%29+=+log%28%28x%29%29-4\"$ and not $\"f%28x%29+=+log%28%28x-4%29%29\"$ , then $\"g%28f%28x%29%29+=+1%2F%28log%28%28x%29%29%29\"$ as shown by the other tutor.
\n" ); document.write( "It's ideal to be careful with parenthesis placement.\r
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\n" ); document.write( "\n" ); document.write( "We cannot have x = 1 as an input since it leads to the denominator log(x) being zero.
\n" ); document.write( "log(1) = 0 for any valid base.\r
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\n" ); document.write( "\n" ); document.write( "We also cannot have x = 0 nor negative x inputs since log(x) has the domain x > 0.
\n" ); document.write( "log(0) = undefined
\n" ); document.write( "log(anything negative) = undefined
\n" ); document.write( "I'll assume your teacher hasn't covered complex numbers quite yet. \r
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\n" ); document.write( "\n" ); document.write( "Answer: $\"x+%3C=+0\"$ or x = 1 lead to g(f(x)) being undefined.
\n" ); document.write( "Or you can expand things out a bit to say: x < 0 or x = 0 or x = 1 are three cases when g(f(x)) is undefined.
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