Answered

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Find [tex]$f(g(x))$[/tex] if:

[tex]\[
\begin{array}{l}
f(x)=2x+5 \\
g(x)=4x-2
\end{array}
\][/tex]

A. [tex]$8x-9$[/tex]
B. [tex]$8x+9$[/tex]
C. [tex][tex]$8x-1$[/tex][/tex]
D. [tex]$8x+1$[/tex]

Sagot :

GinnyAnsweridn
To find [tex]\( f(g(x)) \)[/tex] given the functions [tex]\( f(x) = 2x + 5 \)[/tex] and [tex]\( g(x) = 4x - 2 \)[/tex], follow these steps:

1. Calculate [tex]\( g(x) \)[/tex] :
[tex]\[ g(x) = 4x - 2 \][/tex]

2. Substitute [tex]\( g(x) \)[/tex] into [tex]\( f(x) \)[/tex] to find [tex]\( f(g(x)) \)[/tex] :
[tex]\[ f(g(x)) = f(4x - 2) \][/tex]

3. Substitute [tex]\( 4x - 2 \)[/tex] into the function [tex]\( f(x) \)[/tex] :
[tex]\[ f(4x - 2) = 2(4x - 2) + 5 \][/tex]

4. Simplify the expression:
[tex]\[ 2(4x - 2) + 5 = 2 \cdot 4x + 2 \cdot (-2) + 5 \][/tex]
[tex]\[ = 8x - 4 + 5 \][/tex]
[tex]\[ = 8x + 1 \][/tex]

So, the result of [tex]\( f(g(x)) \)[/tex] is [tex]\( 8x + 1 \)[/tex].

Therefore, among the given options:

- [tex]\( 8x - 9 \)[/tex]
- [tex]\( 8x + 9 \)[/tex]
- [tex]\( 8x - 1 \)[/tex]
- [tex]\( 8x + 1 \)[/tex]

The correct answer is [tex]\( 8x + 1 \)[/tex].
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