Question

The domain of function $f\left(x\right)=\frac{x^2-10x+26}{x^4(x^2-9)(1+27x^2)}$

• A. $x\in R-\{0,\pm 3\}$
• B. $x\in R-\{0,3\}$
• C. $x\in R$
• D. none

Answer 1

Answer: (A)

$x\in R-\{0,\pm 3\}$

$f\left(x\right)=\frac{x^2-10x+26}{x^4(x^2-9)(1+27x^2)}$

The function is defined only when

$x^4(x^2-9)(1+27x^2)\ne 0⟹x\ne 0,x^2-9\ne 0x^2\ne 9x\ne \pm 3$

The domain is $R-\{0,\pm 3\}$