Answer:
The value of (g o f)(3) is 8.
Explanation:
In this problem, we are dealing with composite functions.
A composite function is a function where the output of one function becomes the input of another function.
In this case, we have:
f(x) = 3x - 2
g(x) = x + 1
gof(x) means "g of f(x)".
This means we first apply the function f(x) to the input x, and then apply the function g(x) to the output of f(x).
Here's how we solve the problem step-by-step:
1. Find f(3):
- We substitute x = 3 into the function f(x):
- f(3) = (3 * 3) - 2
- f(3) = 9 - 2
- f(3) = 7
2. Find g(f(3)):
- We know f(3) = 7.
Now, we substitute this value into the function g(x):
- g(f(3)) = g(7)
- g(7) = 7 + 1
- g(7) = 8
Therefore, the value of gof(3) is 8.