Question
The function \( h \) is defined below. \[ h(x) \frac{x^{2}+4 x+3}{x^{2}+8 x+16} \] Find all values of \( x \) that are NOT in the domain of \( h \). If there is more than one value, separate them with commas. \( x=\square . \square \)
Ask by Weston Hilton. in the United States
Mar 13,2025
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\( x = -4 \)
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Bonus Knowledge
To find the values of \( x \) that are not in the domain of the function \( h \), we need to determine when the denominator equals zero. The denominator is given by: \[ x^2 + 8x + 16. \] We can factor this expression: \[ x^2 + 8x + 16 = (x + 4)^2. \] Setting the denominator equal to zero: \[ (x + 4)^2 = 0 \] This implies: \[ x + 4 = 0 \] Thus, \[ x = -4. \] So, the value that is NOT in the domain of \( h \) is: \( x = -4. \)