To find [tex]\( f(-4) \)[/tex] and [tex]\( g(2) \)[/tex] given the functions [tex]\( f(x) = 5x - 1 \)[/tex] and [tex]\( g(x) = -4x^2 - 3 \)[/tex], let's evaluate each function step by step.
### Step 1: Evaluate [tex]\( f(-4) \)[/tex]
The function [tex]\( f(x) \)[/tex] is given by:
[tex]\[ f(x) = 5x - 1 \][/tex]
We'll substitute [tex]\( x = -4 \)[/tex] into the function:
[tex]\[ f(-4) = 5(-4) - 1 \][/tex]
Now, compute the value:
[tex]\[ f(-4) = -20 - 1 = -21 \][/tex]
So, the value of [tex]\( f(-4) \)[/tex] is:
[tex]\[ f(-4) = -21 \][/tex]
### Step 2: Evaluate [tex]\( g(2) \)[/tex]
The function [tex]\( g(x) \)[/tex] is given by:
[tex]\[ g(x) = -4x^2 - 3 \][/tex]
We'll substitute [tex]\( x = 2 \)[/tex] into the function:
[tex]\[ g(2) = -4(2)^2 - 3 \][/tex]
Now, compute the value:
[tex]\[ g(2) = -4(4) - 3 = -16 - 3 = -19 \][/tex]
So, the value of [tex]\( g(2) \)[/tex] is:
[tex]\[ g(2) = -19 \][/tex]
### Final Results
[tex]\[ f(-4) = -21 \][/tex]
[tex]\[ g(2) = -19 \][/tex]
Thus, the simplified answers are:
[tex]\[ f(-4) = -21 \][/tex]
[tex]\[ g(2) = -19 \][/tex]
