Questions: The functions f and g are defined as follows. f(x) = x^2 / (x-2) g(x) = (x-1) / (x^2 - 8x + 7) For each function, find the domain. Write each answer as an interval or union of intervals. Domain of f : Domain of g :

The functions f and g are defined as follows.

f(x) = x^2 / (x-2)

g(x) = (x-1) / (x^2 - 8x + 7)

For each function, find the domain.
Write each answer as an interval or union of intervals.

Domain of f :

Domain of g :

Transcript text: The functions $f$ and $g$ are defined as follows. \[ \begin{array}{l} f(x)=\frac{x^{2}}{x-2} \\ g(x)=\frac{x-1}{x^{2}-8 x+7} \end{array} \] For each function, find the domain. Write each answer as an interval or union of intervals. Domain of $f$ : $\square$ Domain of $g$ : $\square$

Solution

Solution Steps

Step 1: Identify the Denominator Polynomials

For function f(x), the denominator polynomial is Q(x). For function g(x), the denominator polynomial is S(x).

Step 2: Find the Roots of the Denominator Polynomials

The roots of Q(x) are: [2.] The roots of S(x) are: [1. 7.]

Step 3: Determine the Domain

The domain of f(x) is all real numbers except [2.]. The domain of g(x) is all real numbers except [1. 7.].

Final Answer:

f(x) Domain: (-∞, 2) U (2, +∞) g(x) Domain: (-∞,1) U (1, 7) U (7, +∞)

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