The domain of 𝑓(𝑥)=1𝑥2−6𝑥−7f(x)= x 2 −6x−7​ 1​ is:

The domain of a function is the set of all possible input values (often x-values) which will output real numbers.

The function given is 𝑓(𝑥)=1/(𝑥^2−6𝑥−7).

The denominator of this function is a quadratic equation (𝑥^2−6𝑥−7).

For the function to be defined, the denominator cannot be equal to zero (as division by zero is undefined).

So, we need to find the values of x for which 𝑥^2−6𝑥−7 = 0.

This can be done by factoring the quadratic equation or using the quadratic formula.

Factoring gives us (x-7)(x+1) = 0.

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

These are the values that x cannot be, as they would make the denominator zero.

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