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Given the functions [tex]\( f \)[/tex] and [tex]\( g \)[/tex] below, find [tex]\( g(f(0)) \)[/tex].

[tex]\( f(x) = 4x + 1 \)[/tex]

[tex]\( g(x) = 5x - 3 \)[/tex]

Sagot :

GinnyAnswer
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].
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