To find f(g(x)) for f(x) = x² + x + 2 and g(x) = x - 3, substitute g(x) into f(x), expand and simplify to get x² - 5x + 8.
The question asks to find f(g(x)), where f(x) = x² + x + 2 and g(x) = x - 3. To find f(g(x)), you substitute g(x) into every instance of x in f(x). This process is often referred to as composition of functions. The steps are as follows:
Find g(x): g(x) = x - 3.
Substitute g(x) into f(x): f(g(x)) = (x - 3)² + (x - 3) + 2.
Expand and simplify the expression to find the result.
The expanded form would be
Square the binomial: (x - 3)² = x² - 6x + 9.
Add the linear term from g(x) and the constant: -6x + 9 + x - 3 + 2.
Combine like terms: x² - 5x + 8.
Therefore, the function f(g(x)) simplifies to x² - 5x + 8.