f(g(x)) means that you plug in the function of g(x) into x.
It is like plugging in a number for x
f(1) = 3(1) - 2 / 2(1)
But instead of a number, you plug in the function of g(x)
[tex]f(x) = \frac{3x-2}{2x}[/tex]
[tex]f(g(x)) = \frac{3(g(x)) - 2}{2(g(x))}[/tex]
Since you know g(x) = 4x - 1, you replace g(x) with 4x - 1
[tex]f(g(x)) = \frac{3(4x-1)-2}{2(4x-1)}[/tex]
[tex]f(g(x))=\frac{12x-3-2}{8x-2} = \frac{12x - 5}{8x-2}[/tex]
The value of the composite function f(g(x)) is [tex]f(g(x)) = \frac{12x - 5}{2x}[/tex]
We have:
[tex]f(x) = \frac{3x - 2}{2x}[/tex]
g(x) = 4x - 1
We have:
[tex]f(x) = \frac{3x - 2}{2x}[/tex]
Substitute g(x) for x
[tex]f(g(x)) = \frac{3g(x) - 2}{2x}[/tex]
Substitute g(x) = 4x - 1
[tex]f(g(x)) = \frac{3(4x - 1) - 2}{2x}[/tex]
Expand
[tex]f(g(x)) = \frac{12x - 3 - 2}{2x}[/tex]
Evaluate the like terms
[tex]f(g(x)) = \frac{12x - 5}{2x}[/tex]
Hence, the value of f(g(x)) is [tex]f(g(x)) = \frac{12x - 5}{2x}[/tex]
Read more about composite functions at:
https://brainly.com/question/10687170
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