Find the domain for (f+g)(x)(𝑓+𝑔)(𝑥) when f(x)=−x5x−6𝑓(𝑥)=-𝑥5𝑥-6 and g(x)=4x8x−3.𝑔(𝑥)=4𝑥8𝑥-3.

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

For the function f(x) = -x/(5x - 6), the denominator cannot be zero because division by zero is undefined in mathematics. Therefore, we need to find the x-value that makes the denominator zero and exclude it from the domain.

Setting the denominator equal to zero gives:

5x - 6 = 0 5x = 6 x = 6/5 = 1.2

So, the domain of f(x) is all real numbers except x = 1.2.

Similarly, for the function g(x) = 4x/(8x - 3), the denominator cannot be zero.

Setting the denominator equal to zero gives:

8x - 3 = 0 8x = 3 x = 3/8 = 0.375

So, the domain of g(x) is all real numbers except x = 0.375.

The domain of (f+g)(x) is the intersection of the domains of f(x) and g(x). Therefore, the domain of (f+g)(x) is all real numbers except x = 1.2 and x = 0.375.