Question

1. tentukan invers dari fungsi-fungsi berikut ini :
a) f(x) = 2x + 3
b) f(x) = 2x² + 3
2. jika diketahui f(x) = 2 + 3x, tentukan inversnya dan nilai f⁻¹(1) !
3. diketahui f(x) = 5x - 3. jika f⁻¹(a)=2, maka nilai a+5=..........
4. diketahui fungsi f(x) = 3x + 5, g(x) = x-1, tentukanlah ( gof)-1(x) !
5. tentukan fungsi invers dari f(x) = 4x - 3 / 2x + 1

Answer 1

1)
a. f(x)= 2x + 3
 2x+3 = y
2x = y- 3
x =  (y-3)/2
f⁻¹(x)= (x-3)/2

b. f(x)= 2x² +3
2x²+3= y
2x² = y-3
x² = (y-3)/2
x = √{(y-3)/2}
f⁻¹(x) = √{(x-3)/2}

2. 
f(x)= 2 + 3x
2+ 3x = y
3x = y-2
x = (y-2)/3
f⁻¹(x)= (x-2)/3
nilai f⁻¹(1) = (1-2)/3 = -1/3

3.
f(x)= 5x-3
f⁻¹(5x-3) = x --> f⁻¹(a)= 2
5a - 3 = 2
5a= 5
a= 1
a+ 5 = 1+5 = 6

4)
f(x)= 3x+5
g(x) = x-1
(fog)(x) = f {g(x)} = f{x-1) = 3(x-1)+ 5
(fog(x)= 3x + 2
3x +2 = y
3x = y-2
x= (y-2)/3
(fog)⁻¹(x)= (x-2)/3

5.
f(x)= (4x-3)/(2x+1)
f⁻¹(x)= (x + 3)/(-2x + 4)