To solve for [tex]\( f[g(-3)] \)[/tex], we need to follow these steps:
1. First, evaluate [tex]\( g(-3) \)[/tex]:
[tex]\[ g(x) = x - 1 \][/tex]
Substitute [tex]\( x = -3 \)[/tex]:
[tex]\[ g(-3) = -3 - 1 = -4 \][/tex]
So, [tex]\( g(-3) = -4 \)[/tex].
2. Next, we use this result to evaluate [tex]\( f(g(-3)) \)[/tex], which is [tex]\( f(-4) \)[/tex].
[tex]\[ f(x) = 3x + 5 \][/tex]
Substitute [tex]\( x = -4 \)[/tex]:
[tex]\[ f(-4) = 3(-4) + 5 = -12 + 5 = -7 \][/tex]
So, [tex]\( f(-4) = -7 \)[/tex].
By combining these steps, we find:
[tex]\[ f[g(-3)] = f(-4) = -7 \][/tex]
Thus, the final result is:
[tex]\[ f[g(-3)] = -7 \][/tex]
