Given the function [tex]\( f(t) = 2t - 3 \)[/tex], we need to evaluate [tex]\( f(t) \)[/tex] and [tex]\( f(t^2) \)[/tex]. Let's go through the steps to find these values.
### Step 1: Evaluate [tex]\( f(t) \)[/tex]
To evaluate [tex]\( f(t) \)[/tex], we simply substitute [tex]\( t = 1 \)[/tex] into the function [tex]\( f(t) = 2t - 3 \)[/tex]:
[tex]\[ f(1) = 2(1) - 3 = 2 - 3 = -1 \][/tex]
So, [tex]\( f(t) \)[/tex] when [tex]\( t = 1 \)[/tex] is:
[tex]\[ f(1) = -1 \][/tex]
### Step 2: Evaluate [tex]\( f(t^2) \)[/tex]
Next, we need to evaluate [tex]\( f(t^2) \)[/tex]. First, compute [tex]\( t^2 \)[/tex] when [tex]\( t = 1 \)[/tex]:
[tex]\[ t^2 = 1^2 = 1 \][/tex]
Now, we substitute [tex]\( t^2 = 1 \)[/tex] into the function [tex]\( f(t) = 2t - 3 \)[/tex]:
[tex]\[ f(t^2) = f(1) = 2(1) - 3 = 2 - 3 = -1 \][/tex]
So, [tex]\( f(t^2) \)[/tex] when [tex]\( t = 1 \)[/tex] is:
[tex]\[ f(1) = -1 \][/tex]
### Summary
After following these steps, we find that both [tex]\( f(1) \)[/tex] and [tex]\( f(1^2) \)[/tex] are equal to -1:
[tex]\[ f(t) = -1 {\text{ and }} f(t^2) = -1 \][/tex]
