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The set {x:x∈R,x≠−1}

is the domain of which of the following functions?(1 point)
Responses

f(x)=1x−1
f left parenthesis x right parenthesis equals Start Fraction 1 over x End Fraction minus 1

f(x)=13x−3
f left parenthesis x right parenthesis equals Start Fraction 1 over 3 x minus 3 End Fraction

f(x)=12x+2
f left parenthesis x right parenthesis equals Start Fraction 1 over 2 x plus 2 End Fraction

f(x)=12x+1

1 answer

To determine which function has the domain \({x \in \mathbb{R} : x \neq -1}\), we need to identify any restrictions in the domain of each function.

  1. \(f(x) = \frac{1}{x - 1}\):

    • Here, the function is undefined when \(x - 1 = 0\) (i.e., \(x = 1\)).
    • The domain is \({x \in \mathbb{R} : x \neq 1}\).

  2. \(f(x) = \frac{1}{3x - 3}\):

    • This function is undefined when \(3x - 3 = 0\) (i.e., \(x = 1\)).
    • The domain is \({x \in \mathbb{R} : x \neq 1}\).

  3. \(f(x) = \frac{1}{2x + 2}\):

    • This function is undefined when \(2x + 2 = 0\) (i.e., \(x = -1\)).
    • The domain is \({x \in \mathbb{R} : x \neq -1}\).

  4. \(f(x) = \frac{1}{2x + 1}\):

    • This function is undefined when \(2x + 1 = 0\) (i.e., \(x = -\frac{1}{2}\)).
    • The domain is \({x \in \mathbb{R} : x \neq -\frac{1}{2}}\).

Based on this analysis, the function that has the domain \({x \in \mathbb{R} : x \neq -1}\) is:

\(f(x) = \frac{1}{2x + 2}\).