Exercise Zone : Invers Fungsi

Berikut ini adalah kumpulan soal mengenai Invers Fungsi. Jika ingin bertanya soal, silahkan gabung ke grup Telegram, Signal, Discord, atau WhatsApp.

Tipe:

Standar SBMPTN HOTS

No.

Tentukan f^{-1}(x) dari {f(x)=\dfrac{3x+5}{2x-3}}

dari Nasywa

$$\begin{array}{rl}f(x)& ={\displaystyle \frac{3x+5}{2x-3}}\\ y& ={\displaystyle \frac{3x+5}{2x-3}}\\ (2x-3)y& =3x+5\\ 2xy-3y& =3x+5\\ 2xy-3x& =3y+5\\ x(2y-3)& =3y+5\\ x& ={\displaystyle \frac{3y+5}{2y-3}}\\ f^{-1}(x)& =\boxed{{\displaystyle \boxed{{\displaystyle {\displaystyle \frac{3x+5}{2x-3}}}}}}\end{array}$$

Jadi, f^{-1}(x)=\dfrac{3x+5}{2x-3}.

No.

Diketahui fungsi f dengan rumus {f(x)=3x+1} dan f^{-1}(x) adalah fungsi invers dari f(x). Nilai dari f^{-1}(7)= ....

1. 1
2. 2
3. 3

4. 4
5. 11

Misal f^{-1}(7)=x
$$\begin{array}{rl}f(x)& =7\\ 3x+1& =7\\ 3x& =6\\ x& =2\\ f^{-1}(7)& =\boxed{{\displaystyle \boxed{{\displaystyle 2}}}}\end{array}$$

Jadi, f^{-1}(7)=2. JAWAB: B

No.

fungsi invers f^{-1}(x) dari {f(x)=2^{3x}} adalah

1. \dfrac13
2. B
3. C

4. D
5. E

SKB CPNS MATEMATIKA 2020

$$\begin{array}{rl}y& =2^{3x}\\ 3x& ={}^2\log y\\ x& ={\displaystyle \frac{1}{3}}{}^2\log y\\ f^{-1}(x)& ={\displaystyle \frac{1}{3}}{}^2\log x\end{array}$$

Jadi, f^{-1}(x)=\dfrac13\ {^2\negmedspace\log x}.

No.

Tentukan rumus fungsi invers untuk fungsi f(x) = \dfrac{2x+5}{3x-1}​

brainly.co.id

$$\begin{array}{rl}y& ={\displaystyle \frac{2x+5}{3x-1}}\\ (3x-1)y& =2x+5\\ 3xy-y& =2x+5\\ 3xy-2x& =y+5\\ x(3y-2)& =y+5\\ x& ={\displaystyle \frac{y+5}{3y-2}}\\ f^{-1}(x)& =\boxed{{\displaystyle \boxed{{\displaystyle {\displaystyle \frac{x+5}{3x-2}}}}}}\end{array}$$

Jadi, rumus fungsi invers untuk fungsi f(x) = \dfrac{2x+5}{3x-1}​ adalah f^{-1}(x)=\dfrac{x+5}{3x-2}

No.

Diketahui f:R→ R dan g: R→ R dengan f(x) = \dfrac{x-4}{x+3} dan g(x) = 3x - 2, tentukan \left(f\circ g\right)^{-1} (x)!

brainly.co.id

$$\begin{array}{rl}(f\circ g)(x)& =f(g(x))\\ & =f(3x-2)\\ & ={\displaystyle \frac{3x-2-4}{3x-2+3}}\\ y& ={\displaystyle \frac{3x-6}{3x+1}}\\ (3x+1)y& =3x-6\\ 3xy+y& =3x-6\\ 3xy-3x& =-y-6\\ x(3y-3)& =-y-6\\ x& ={\displaystyle \frac{-y-6}{3y-3}}\\ (f\circ g{)}^{-1}(x)& ={\displaystyle \frac{-x-6}{3x-3}}\end{array}$$

Jadi, \left(f\circ g\right)^{-1} (x)=\dfrac{-x-6}{3x-3}.

No.

Diketahui f(x)= \dfrac{3x+1}{x-5}, x \ne 5. jika f^{-1} (x) merupakan invers f(x). nilai f^{-1} (11) adalah....

brainly.co.id

$$\begin{array}{rl}f(x)& ={\displaystyle \frac{3x+1}{x-5}}\\ y& ={\displaystyle \frac{3x+1}{x-5}}\\ (x-5)y& =3x+1\\ xy-5y& =3x+1\\ xy-3x& =5y+1\\ x(y-3)& =5y+1\\ x& ={\displaystyle \frac{5y+1}{y-3}}\\ f^{-1}(x)& ={\displaystyle \frac{5x+1}{x-3}}\\ f^{-1}(11)& ={\displaystyle \frac{5(11)+1}{11-3}}\\ & ={\displaystyle \frac{55+1}{8}}\\ & ={\displaystyle \frac{56}{8}}\\ & =\boxed{{\displaystyle \boxed{{\displaystyle 7}}}}\end{array}$$

Jadi, f^{-1} (11)=7

No.

Diketahui f(a)=12a+4 dan g(a)= 5a-2 tentukan \left(g^{-1}\circ f^{-1}\right)(a)​

Brainly.co.id

$$\begin{array}{rl}(f\circ g)(x)& =f(g(x))\\ & =f(5a-2)\\ & =12(5a-2)+4\\ & =60a-24+4\\ & =60a-20\end{array}$$

$$\begin{array}{rl}(g^{-1}\circ f^{-1})(x)& =(f\circ g{)}^{-1}(x)\\ & =\boxed{{\displaystyle \boxed{{\displaystyle {\displaystyle \frac{a+20}{60}}}}}}\end{array}$$

Jadi, \left(g^{-1}\circ f^{-1}\right)(a)​=\dfrac{a+20}{60}.