diketahui f(x)=5x-9,g(x)=x²-3 dan h(x)= [tex] (\frac{f}{g} )(x)[/tex] tentukan : a. rumus fungsi h dan b. rumus komposisi (foh)(x)

[tex]h(x) = ( \frac{f}{g} )(x) = \frac{5x - 9}{ {x}^{2} - 3 } \\ (fogoh)(x) = 5( {x}^{2} - 3) + 9 = 5 {x}^{2} - 6[/tex]

f(x) = 5x - 9
g(x) = x^2 - 3
h(x) = (f/g)(x)

a) h(x)
b) (f○h)(x)

a)
h(x) = (f/g)(x)
h(x) = (5x - 9)/(x^2 - 3)

Jadi rumus fungsi h adalah h(x) = (5x - 9)/(x^2 - 3)

b)
(f○h)(x) = f(h(x))
(f○h)(x) = f((5x - 9)/(x^2 - 3))
(f○h)(x) = 5((5x - 9)/(x^2 - 3)) - 9
(f○h)(x) = (25x - 45)/(x^2 - 3) - 9
(f○h)(x) = [(25x - 45)/(x^2 - 3)] - [9(x^2 - 3)/(x^2 - 3)]
(f○h)(x) = [(25x - 45)/(x^2 - 3)] - [(9x^2 - 27)/(x^2 - 3)]
(f○h)(x) = [(25x - 45) - (9x^2 - 27)]/(x^2 - 3)
(f○h)(x) = (25x - 45 - 9x^2 + 27)/(x^2 - 3)
(f○h)(x) = (16x^2 - 18)/(x^2 - 3)

Jadi rumus komposisi (f○h)(x) adalah (f○h)(x) = (16x^2 - 18)/(x^2 - 3)