Let f(x) = x^2 + 5 and g(x) = x – 7. Perform each function operation. Then find the domain of each.

Question

1. f(x)/g(x)
2. f(x)-2g(x)
3. f(x)*g(x)

Answer 1

1. f(x)/g(x) = (x^2 + 5)/(x - 7)
The domain of f(x)/g(x) is all real numbers except x=7, because division by zero is undefined. So the domain is: x ∈ ℝ, x ≠ 7.

2. f(x) - 2g(x) = (x^2 + 5) - 2(x - 7) = x^2 + 5 - 2x + 14 = x^2 - 2x + 19
The domain of f(x)-2g(x) is all real numbers, because there are no restrictions on the values of x for this expression. So the domain is: x ∈ ℝ.

3. f(x)*g(x) = (x^2 + 5)(x - 7) = x^3 - 7x^2 + 5x - 35
The domain of f(x)*g(x) is all real numbers because there are no restrictions on the values of x for this expression. So the domain is: x ∈ ℝ.