diketahui fungsi f(x) = x²-3x dan g(x) = 4x²+2 carilah fog(x) dan gof(x) nya

Diket : f (x) = x² - 3x , g (x) = 4x² + 2

Penyelesaian :
---------------------

fog (x) = f {g (x)}
= f (4x² + 2)
= (4x² + 2)² - 3 (4x² + 2)
= (16x⁴ + 8x² + 8x² + 4) - 12x² - 6
= 16x⁴ + 16x² + 4 - 12x² - 6
= 16x⁴ + 16x² - 12x² + 4 - 6
= 16x⁴ + 4x² - 2

gof (x) = g {f (x)}
= g (x² - 3x)
= 4 (x² - 3x)² + 2
= 4 (x⁴ - 6x³ + 9x²) + 2
= 4x⁴ - 24x³ + 36x² + 2

f(x) = x² - 3x
g(x) = 4x² + 2

(fog)(x) = f(g(x))
            = f(4x² + 2)
            = (4x² + 2)² - 3(4x² + 2)
            = 16x⁴ + 16x² + 4 - 12x² - 6
            = 16x⁴ + 4x² - 2

(gof)(x) = g(f(x))
            = g(x² - 3x)
            = 4(x² - 3x)² + 2
            = 4(x⁴ - 6x³ + 9x²) + 2
            = 4x⁴ - 24x³ + 36x² + 2