To find [tex]\( g(f(0)) \)[/tex] given the functions [tex]\( f(x) = 4x + 1 \)[/tex] and [tex]\( g(x) = 5x - 3 \)[/tex], we need to follow these steps:
1. Evaluate [tex]\( f(0) \)[/tex]:
[tex]\[
f(x) = 4x + 1
\][/tex]
Substitute [tex]\( x = 0 \)[/tex]:
[tex]\[
f(0) = 4(0) + 1 = 1
\][/tex]
2. Use the result of [tex]\( f(0) \)[/tex] to find [tex]\( g(f(0)) \)[/tex]:
We have found that [tex]\( f(0) = 1 \)[/tex].
3. Evaluate [tex]\( g(1) \)[/tex]:
[tex]\[
g(x) = 5x - 3
\][/tex]
Substitute [tex]\( x = 1 \)[/tex]:
[tex]\[
g(1) = 5(1) - 3 = 5 - 3 = 2
\][/tex]
Therefore, [tex]\( g(f(0)) = g(1) = 2 \)[/tex].
Summarizing the results:
- [tex]\( f(0) = 1 \)[/tex]
- [tex]\( g(f(0)) = 2 \)[/tex]
So, [tex]\( g(f(0)) = 2 \)[/tex].
