Let's solve the problem step-by-step using the function [tex]\( f(x) = 3x - 4 \)[/tex].
### Step 1: Understand the problem
We need to find the value of the function [tex]\( f \)[/tex] when the input is [tex]\( r + 3 \)[/tex]. In other words, we are looking to compute [tex]\( f(r + 3) \)[/tex].
### Step 2: Substitute the input into the function
The function [tex]\( f(x) = 3x - 4 \)[/tex] tells us how to transform any input [tex]\( x \)[/tex]. When the input [tex]\( x \)[/tex] is replaced with [tex]\( r + 3 \)[/tex], we get:
[tex]\[ f(r + 3) = 3(r + 3) - 4 \][/tex]
### Step 3: Simplify the expression
Now, let's simplify the expression step-by-step:
1. Distribute the 3 within the parentheses:
[tex]\[ 3(r + 3) = 3r + 9 \][/tex]
2. Substitute back into the function:
[tex]\[ f(r + 3) = 3r + 9 - 4 \][/tex]
3. Combine the constant terms:
[tex]\[ 3r + 9 - 4 = 3r + 5 \][/tex]
### Step 4: Conclusion
The value of [tex]\( f(r + 3) \)[/tex] is:
[tex]\[ f(r + 3) = 3r + 5 \][/tex]
So, we have successfully found that [tex]\( f(r + 3) = 3r + 5 \)[/tex].
