Question

Let f(x) = x² - 4 and g(x) = 1 - x. Find a formula for h(x) = f(g(x)) + g(f(x)) in terms of x, h(x) = ?

If f(x) = 3x + 2, g(x) = 13 - 2x, and h(x) = 5x², then find and simplify the answer?

Answer 1

The formula for h(x) = f(g(x)) + g(f(x)) using functions f(x) = x² - 4 and g(x) = 1 - x is solved step by step and simplifies to h(x) = -2x + 2. The second part of the question appears unrelated to the first and lacks sufficient context for a solution.

Step-by-step explanation:

First, we need to address the original question: Find a formula for h(x) = f(g(x)) + g(f(x)). Using the given functions f(x) = x² - 4 and g(x) = 1 - x, we proceed by plugging g(x) into f(x) and vice versa.

f(g(x)) can be written as f(1-x) which equals (1 - x)² - 4. Similarly, g(f(x)) translates to g(x² - 4) which equals 1 - (x² - 4).

Now, combining these two results we have:

h(x) = (1 - x)² - 4 + 1 - (x² - 4)

Simplifying, we'll get:

h(x) = 1 - 2x + x² - 4 + 1 - x² + 4

Which simplifies further to:

h(x) = -2x + 2

As for the second part of the question, it appears to be based on a different set of functions f(x) = 3x + 2, g(x) = 13 - 2x, and h(x) = 5x². Since this does not seem to match the first part, we'll need clarification or more context to provide an accurate answer for this part.