Question

If f(x) = x² and g(x) = x - 7, find g ° f(x).

Answer 1

To find the composition g ◦ f(x), where f(x) = x² and g(x) = x - 7, we first apply f(x) to get x² and then apply g to that result, yielding the composition g(f(x)) = x² - 7.

Step-by-step explanation:

The question is asking to find the composition of two functions, specifically g ◦ f(x), where f(x) = x² and g(x) = x - 7. To find the composition g ◦ f(x), we must first evaluate f(x) and then apply g to the result of f(x).

Following the composition rule, we find:

1. Calculate f(x), which is x².
2. Now, substitute that into g(x), so we replace every x in g(x) with x², giving us g(f(x)) which is equivalent to (x²) - 7.

Therefore, the composition g ◦ f(x) is equal to x² - 7.