Question

For f(x) = x° - 1 and g(x) = 2x² +7 find each of the following functions and state its domain.

a) f + 9
b) f - 9
c) f * 9
d) f / g
e) g / f

Answer 1

To find the functions and their domains, perform the given operations on the functions f(x) and g(x), and consider any domain restrictions for division. The domains of f + 9, f - 9, and f * 9 are all real numbers. The domain of f / g excludes -√2 and √2, and the domain of g / f excludes 1.

Step-by-step explanation:

To find the functions and their domains, we need to perform the given operations on the functions f(x) and g(x).

1. f + 9: Add 9 to each term of f(x) to get (x° + 9) - 1 = x° + 8. The domain remains the same as f(x) which is all real numbers.
2. f - 9: Subtract 9 from each term of f(x) to get (x° - 9) - 1 = x° - 10. The domain remains the same as f(x) which is all real numbers.
3. f * 9: Multiply each term of f(x) by 9 to get 9x° - 9. The domain remains the same as f(x) which is all real numbers.
4. f / g: Divide f(x) by g(x) which is (x° - 1) / (2x² + 7). The domain is restricted to exclude any values of x that make the denominator zero, so x cannot be -√2 or √2.
5. g / f: Divide g(x) by f(x) which is (2x² + 7) / (x° - 1). The domain is restricted to exclude any values of x that make the denominator zero, so x cannot be 1.