Find the domain for (f−g)(x)(𝑓-𝑔)(𝑥) when f(x)=−8x5x+7𝑓(𝑥)=-8𝑥5𝑥+7 and g(x)=4x−9x−7.𝑔(𝑥)=4𝑥-9𝑥-7.

The domain of a function is the set of all possible input values (often the "x" variable), which will produce a valid output from a particular function.

The domain of (f-g)(x) is the set of all x such that x is in the domain of f and x is in the domain of g.

The given functions are f(x) = -8x/(5x+7) and g(x) = 4x/(x-7).

For the function f(x), the denominator cannot be zero because division by zero is undefined. So, we set the denominator equal to zero and solve for x:

5x + 7 = 0 5x = -7 x = -7/5

So, the domain of f(x) is all real numbers except x = -7/5.

For the function g(x), similarly, the denominator cannot be zero. So, we set the denominator equal to zero and solve for x:

x - 7 = 0 x = 7

So, the domain of g(x) is all real numbers except x = 7.

Therefore, the domain of (f-g)(x) is all real numbers except x = -7/5 and x = 7.