The expression under the square root must be non-negative.

To find the domain of the function f(x) = sqrt(x+7)x^2-4, we need to consider two conditions: Step 1: The expression under the square root must be non-negative. For sqrt(x+7) to be defined, we must have: x+7 0 x -7 Step 2: The denominator cannot be zero. For the fraction to be defined, the denominator x^2-4 cannot be equal to zero: x^2-4 0 We can factor the denominator as a difference of squares: (x-2)(x+2) 0 This means that: x-2 0 x 2 x+2 0 x -2 Step 3: Combine the conditions. We need to satisfy both x -7 and x 2 and x -2. The interval x -7 is [-7, ). From this interval, we must exclude the values x=2 and x=-2. Both of these values are within the interval [-7, ). So, the domain of f(x) is all x such that x -7 but x -2 and x 2. In interval notation, this is: [-7, -2) (-2, 2) (2, ) The domain of f(x) is [-7, -2) (-2, 2) (2, ). Send me the next one 📸