Diberikan f(x) = 6/(x - 4), x ≠ 4 , dan (g o f) = ...

Question

Diberikan f(x) = 6/(x - 4), x ≠ 4 , dan (g o f) = (2x + 5)/(x - 4), x ≠ 4. Tentukan rumus g(x) = ...

Dita F · Accepted Answer

diket : f(x) = 6/(x-4)   x≠4
            (gof) = (2x+5)/(x-4)   x≠4
tanya : rumus g(x)
jawab :
f(x) = 6/x-4
y = 6/x-4
y(x-4) = 6
xy - 4y = 6
xy = 6 + 4y
x = 6 + 4y/y
f'¹(x) = 6+4x/x

g(x) = (gof) (f'¹(x))
        = (gof) (6+4x/x)
        = 2(6+4x/x) +5 : (6+4x/x) -4
        = (12+8x/x)+5 : (6+4x/x) -4
        = 12+8x+5x/x : 6+4x-4x/x
        = 12+13x/x : 6/x
        = (12+13x/x) x (x/6)
g(x) = 12+13x/6

Jukus J · Answer

(gof) (x) =g(f(x)
(2x+5)/(x-4) = g(6/x-4)
                             6/x-4=a/1
                             6=ax-4a
                             6+4a=ax
                             6+4a=a(x)
                             6+4a/a=x
2(6+4a/a)+ 5 /(6+4a/a)-4=g(a)
(12+8a/a + 5(a)) /(6+4a/a)-4(a)= g(a)
(12+13a/a):6/a
(12+13a/a)×a/6
12+13a2/6a=12+13a/6(a2 dan a dicoret)

Jukus J · Answer

12+13a/6=g(a)
12+13x/6=g(x)
lanjutan yg tadi

Diberikan f(x) = 6/(x - 4), x ≠ 4 , dan (g o f) = (2x + 5)/(x - 4), x ≠ 4. Tentukan rumus g(x) = ...

(gof) (x) =g(f(x) (2x+5)/(x-4) = g(6/x-4) 6/x-4=a/1 6=ax-4a 6+4a=ax 6+4a=a(x) 6+4a/a=x 2(6+4a/a)+ 5 /(6+4a/a)-4=g(a) (12+8a/a + 5(a)) /(6+4a/a)-4(a)= g(a) (12+13a/a):6/a (12+13a/a)×a/6 12+13a2/6a=12+13a/6(a2 dan a dicoret)

12+13a/6=g(a) 12+13x/6=g(x) lanjutan yg tadi

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