Question

Find the domain and range of f(x ) = (x^2+2x+1)/(x^2-8x+12)

Answer 1

The range of a parabola that opens up starts at its vertex (1,−9)(1,-9) and extends to infinity.[−9,∞)[-9,∞){y|y≥−9}{y|y≥-9}Determine the domain and range.Domain: (−∞,∞),{x|x∈R}(-∞,∞),{x|x∈ℝ} for any integer nnRange: [−9,∞),{y|y≥−9}

Answer 2

SOLUTION ⚜️

$given \: f(x) = \frac{ {x}^{2} + 2x + 1 }{ {x}^{2} - 8x + 12}$

Here, f(x) is an rational function of x as$\frac{ {x}^{2} + 2x + 1 }{ {x}^{2} - 8x + 12}$is rational expression.

$\therefore f(x) \: assumes \: real \: values \: x \: espects \\ for \: the \: values \: of \: x \: for \: which \: {x}^{2} - 8x + 12 = 0$

$i.e.,(x - 6)(x - 2) = 0 \rightarrow x = 6,2 \\ \therefore domain \: of \: f(x)$

= R-{2,6}