The domain of 𝑓(𝑥)=1𝑥2−6𝑥−7f(x)= x 2 −6x−7​ 1​ is:A.(1, 7)B.(−∞,−1]∪[7,∞)(−∞,−1]∪[7,∞)C.[-1, 7]D.x > -1 or x < 7E.{x<−1}∪{x>7}{x<−1}∪{x>7}

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

The function 𝑓(𝑥)=1/(𝑥^2−6𝑥−7) is a rational function, and rational functions are undefined where the denominator is equal to zero.

So, to find the domain of this function, we first need to find the values of x that make the denominator zero. We do this by setting the denominator equal to zero and solving for x:

𝑥^2−6𝑥−7 = 0

This is a quadratic equation, and we can solve it by factoring:

(x - 7)(x + 1) = 0

Setting each factor equal to zero gives the solutions x = 7 and x = -1.

These are the values that make the denominator zero, so they are the values that are NOT in the domain of the function.

Therefore, the domain of the function is all real numbers except x = -1 and x = 7.

In interval notation, this is written as (-∞, -1) ∪ (-1, 7) ∪ (7, ∞), which corresponds to option B.