Question

If f(x) = x² - 1, and g(x) = x + 2, then g(f(x)) = [?]x² +
please explain ​

Answer 1

g(f(x)) = x² + 1.

Explanation:

To evaluate g(f(x)), we need to first evaluate f(x) and then plug the result into g(x). Since f(x) = x² - 1, we have g(f(x)) = g(x² - 1). Plugging this into g(x), we get g(x² - 1) = (x² - 1) + 2. So the final result is g(f(x)) = x² + 1.

Here's a step-by-step breakdown:

1. g(f(x)) = g(x² - 1) [substitute f(x) = x² - 1]
2. g(f(x)) = (x² - 1) + 2 [substitute g(x) = x + 2]
3. g(f(x)) = x² + 1 [simplify]

Note that this is only the case if f(x) and g(x) are defined for all values of x. If either function is only defined for certain values of x, then the result of g(f(x)) will depend on the specific input value used.