Solving the Problem: f(g(-1))

In this article, we will explore the concept of function composition and learn how to solve the problem 'f(g(-1))' where f(x) = 2x^2 - 2 and g(x) = 5x + 1.

Understanding Function Composition

Function composition is the process of combining two or more functions to create a new function. The new function, denoted as (f ∘ g)(x), represents the result of applying the function g(x) and then applying the function f(x) to the result.

In other words, if we have two functions f(x) and g(x), the composition of these functions, (f ∘ g)(x), is defined as:

(f ∘ g)(x) = f(g(x))

Solving the Problem: f(g(-1))

To find the value of f(g(-1)), we need to follow these steps:

1. Substitute -1 for x in the function g(x) to find the value of g(-1).
2. Substitute the value of g(-1) into the function f(x) to find the value of f(g(-1)).

Step 1: Find the value of g(-1). g(x) = 5x + 1 g(-1) = 5(-1) + 1 = -5 + 1 = -4

Step 2: Find the value of f(g(-1)). f(x) = 2x^2 - 2 f(g(-1)) = f(-4) = 2(-4)^2 - 2 = 2(16) - 2 = 32 - 2 = 30

Therefore, the value of f(g(-1)) is 30.

By understanding the concept of function composition and following the step-by-step process, you can solve problems involving the composition of functions, such as f(g(-1)).