Question

If f (x) = -12x⁴ + 5x² – 45 and g(x) = 10x⁴ – 70x² – 300, what is (f -g) (x)?

Answer 1

To find (f - g)(x), subtract g(x) from f(x) and simplify the expression.

Step-by-step explanation:

The expression (f - g)(x) represents the difference between the functions f(x) and g(x). To find (f - g)(x), we subtract the function g(x) from f(x). Given that f(x) = -12x⁴ + 5x² - 45 and g(x) = 10x⁴ - 70x² - 300, we substitute these expressions into (f - g)(x) and simplify.

(f - g)(x) = (-12x⁴ + 5x² - 45) - (10x⁴ - 70x² - 300)

Expanding the brackets, we get:

(f - g)(x) = -12x⁴ + 5x² - 45 - 10x⁴ + 70x² + 300

Combining like terms, we have:

(f - g)(x) = -22x⁴ + 75x² + 255