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Consider these functions:

[tex]\[
\begin{array}{l}
f(x) = 2x^3 + 3 \\
g(x) = x - 4
\end{array}
\][/tex]

What is the value of [tex]\( g(f(x)) \)[/tex]?

Sagot :

GinnyAnswer
To find the value of [tex]\( g(f(x)) \)[/tex], we need to substitute the function [tex]\( f(x) \)[/tex] into [tex]\( g(x) \)[/tex].

1. Given functions:
[tex]\[ f(x) = 2x^3 + 3 \][/tex]
[tex]\[ g(x) = x - 4 \][/tex]

2. We need to evaluate [tex]\( g(f(x)) \)[/tex], i.e., to apply function [tex]\( g \)[/tex] to the result of [tex]\( f(x) \)[/tex].

3. First, calculate [tex]\( f(x) \)[/tex]:
[tex]\[ f(x) = 2x^3 + 3 \][/tex]

4. Next, substitute [tex]\( f(x) \)[/tex] into [tex]\( g(x) \)[/tex] where [tex]\( x \)[/tex] in [tex]\( g(x) \)[/tex] becomes [tex]\( 2x^3 + 3 \)[/tex]:
[tex]\[ g(f(x)) = g(2x^3 + 3) \][/tex]
Since [tex]\( g(x) = x - 4 \)[/tex], replace [tex]\( x \)[/tex] with [tex]\( 2x^3 + 3 \)[/tex]:
[tex]\[ g(2x^3 + 3) = (2x^3 + 3) - 4 \][/tex]

5. Simplify the expression:
[tex]\[ (2x^3 + 3) - 4 = 2x^3 + 3 - 4 = 2x^3 - 1 \][/tex]

Therefore, the value of [tex]\( g(f(x)) \)[/tex] is:
[tex]\[ g(f(x)) = 2x^3 - 1 \][/tex]
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