Paul works for a company that deals in paints and dyes. he is paid a fixed monthly salary plus 15 percent commission on monthly sales over $20,000. if paul manages to achieve total monthly sales of $x, which is over $20,000, the function f(x) representing paul's monthly sales over $20,000 is given by . if x is the sales amount over $20,000, the function g(x) giving paul's commission is . the function g(f(x)) representing paul's commission on monthly sales above $20,000, where x is paul's total monthly sales amount, is given by . if paul's sales in a particular month are $27,500, his commission for the month is $.

Given that Paul works for a company that deals in paints and dyes. He is paid a fixed monthly salary plus 15 percent commission on monthly sales over $20,000.

If Paul manages to achieve total monthly sales of $x, which is over $20,000, the function f(x) representing Paul's monthly sales over $20,000 is given by
f(x) = x - 20,000.

If x is the sales amount over $20,000, the function g(x) giving Paul's commission is given by
g(x) = 15% of x = 0.15x.
Therefore, the function g(x) giving Paul's commission is given by
g(x) = 0.15x.

The function g(f(x)) representing Paul's commission on monthly sales above $20,000, where x is Paul's total monthly sales amount, is given by
g(f(x)) = 0.15(x - 20,000) = 0.15x - 3,000.
Therefore, the function g(f(x)) representing Paul's commission on monthly sales above $20,000, where x is Paul's total monthly sales amount, is given by
g(f(x)) = 0.15x - 3,000.

If Paul's sales in a particular month are $27,500, recall, that the function representing Paul's commission is given by
g(f(x)) = 0.15x - 3,000.
Therefore, his commission for the month he made $27,500 in sales is given by 0.15(27,500) - 3,000 = 4,125 - 3000 = $1,125.