Find the domain of the composite function f degreeg fx 8x8g

Find the domain of the composite function f degreeg. f(x) = 8/x-8;g(x) =9/x Select the correct choice below and fill in any answer boxes within your choice. A. The domain is {x| }. (Type an inequality. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The domain is all real numbers.

Solution

f(x) = 8 / (x-8) ; g(x) = 9/x

fog(x) = plug g(x) into f(x)

fog(x) = 8 /{ ( 9/x) - 8 }

fog(x) = 8x / ( 9-8x)

therefore, domain of the function fog(x) = all values of x except x not equal to 9/8 , x not equal to 0