Answer:
[tex]f(x) = \frac{2x}{2x + 3}[/tex]
Step-by-step explanation:
Given
[tex]h(x) = \frac{2x + 3}{x}[/tex]
[tex]g(x) = \frac{2}{x}[/tex]
[tex]g(f(x)) = h(x)[/tex]
Required
Find f(x)
[tex]g(x) = \frac{2}{x}[/tex]
Substitute x for f(x)
[tex]g(f(x)) = \frac{2}{f(x)}[/tex]
Recall that
[tex]g(f(x)) = h(x)[/tex]
This gives
[tex]\frac{2}{f(x)} = \frac{2x + 3}{x}[/tex]
Cross Multiply
[tex]f(x) * (2x + 3) = 2 * x[/tex]
[tex]f(x) * (2x + 3) = 2 x[/tex]
Make f(x) the subject of formula
[tex]f(x) = \frac{2x}{2x + 3}[/tex]
