Matematika Sekolah Menengah Atas Jika f(x - 2) = 2x-3/3x+4, maka f^-1(1) = ... A. -6 B. -7 C. -8 D. -9 E. -10 ​

priscillaarmstrongulv – March 21, 2023

Jika f(x - 2) = 2x-3/3x+4, maka f^-1(1) = ...
A. -6
B. -7
C. -8
D. -9
E. -10 ​

Jawab:

fungsi invers

f(x) = y   ⇒ f⁻¹(y) = x

[tex]\rm f(x- 2) = \dfrac{2x-3}{3x+4}[/tex]

[tex]\rm f(x) = \dfrac{2(x+2)-3}{3(x+2) + 4}= \dfrac{2x+4 - 1}{3x+6+4}[/tex]

[tex]\rm f(x)= \dfrac{2x+3}{3x+10}[/tex]

f⁻¹(1)=  x   ⇒  f(x) = 1

[tex]\rm \dfrac{2x+3}{3x+10}= 1[/tex]

3x+ 10 =  2x+ 3

3x - 2x=  3- 10

x= - 7

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