Tugas Math Bu Alfi (kiky).docx

1. f—1 (x) menyatakan invers fungsi f(x). Jika f(x) = 3x-2, maka f-1(x) = .... jawab: f(x)= 3x-2 y= 3x-2 3x=y+2 X=

𝑦+2 3

f-1(x)=

𝑥+2 3

2. g-1(x) menyatakan invers fungsi g(x). Jika g-1(x) = 7-5x, maka g(x) = ..... jawab: g-1(x)= 7 - 5x y= 7-5x 5x= 7-y X=

7−𝑦 5 7−𝑥 5

g(x)=

5𝑥+2

2

3. Jika f(x) = 3𝑥−2 , x ≠ 3 , maka f-1(x) = ..... jawab: 5𝑥+2

f(x)= 3𝑥−2 y=

5𝑥+2 3𝑥−2

3xy-2y= 5x+2 3xy-5x = 2+2y X(3y-5)= 2+2y 2+2𝑦

5

X=3𝑦−5

y≠ 3

2+2𝑥

5

f-1(x) = 3𝑦−5 x≠ 3 4. Jika R(x) =

3𝑥+2 4𝑥

Jawab: 3𝑥+2 4𝑥 3𝑥+2 y= 4𝑥

R(x)=

4xy = 3x+2 4xy-3x = 2 x(4y-3) = 2 2

x = 4𝑦−3 R-1(x) =

2 4𝑥−3

R-1(1) = 2

, maka R-1(1) = .....

3𝑥

5. Jika T(x) = 5𝑥−2 , maka T-1(x) = ...... Jawab: 3𝑥

T(x) = 5𝑥−2 3𝑥

y = 5𝑥−2 5xy-2y = 3x 5xy-3x = 2y x(5y-3) = 2y 2𝑦

x = 5𝑦−3 2𝑥

T-1(x) = 5𝑥−3 1

6. Jika f(x) = 4x+2 untuk semua x, maka f-1(2) = ..... Jawab: f(x) = 4x+2 y = 4x+2 4x-y = 2 x=

𝑦−2 4

𝑥−2 4 1/2−2 -1 1 f ( )= 2 4

f-1(x) =

=−

3 8

7. Diketahui R(x) = x3 – 4 , maka invers dari R adalah ..... Jawab: R(x) = x3 – 4 y = x3 – 4 x3 = y+4 x = 3√𝑦 + 4 3

f-1(x) = √𝑥 + 4 8. Jika T(3x2 + 2 – 3x) = 5x + 7 , maka T-1(12) =...... Jawab: 9. Jika v(t) =

𝑡−1 untuk 4−𝑡

Jawab: 𝑡−1 4−𝑡 𝑡−1 4−𝑡

v(t) = y=

4y-ty = t-1 t+ty = 4y+1 t(1+y) = 4y+1 t=

4𝑦+1 1+𝑦

t ≠ 4, maka v-1(2) = .......

4𝑡+1 1+𝑡 8+1 = 1+2 =

v-1(t) = v-1(2)

3

10. Jika k-1(x) = 43x-7 dan k(t) =2, maka t sama dengan ..... Jawab: k-1(x) = 43x-7 y = 43x-7 y = 26x-14 6x-14 =2 log 𝑦 6x = 2 log 𝑦 + 14 2 log 𝑦+14 6 2 log 𝑥+14 k(x) = 6

x=

11. Jika N(t) = 2 2t-1 -1