J's answer to Intan's Malaysia question.
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f(x) = 3x + 5
Replace f(x) with x and x with f(x).
x = 3f(x) + 5
x - 5 = 3f(x)
⅓x - 5/3 = f(x)
Therefore, the inverse function is :
f-¹(x) = ⅓x - 5/3
This is the function that maps Q to P
Check : f-¹f(x) = f-¹(3x + 5) = ⅓(3x+5) - 5/3 = x + 5/3 - 5/3 = x
Alternatively,
f(x) = 3x + 5
3x = f(x) - 5
x = ⅓f(x) - 5/3
The inverse function is : f-¹(x) = ⅓x - 5/3
Replace f(x) with x and x with f(x).
x = 3f(x) + 5
x - 5 = 3f(x)
⅓x - 5/3 = f(x)
Therefore, the inverse function is :
f-¹(x) = ⅓x - 5/3
This is the function that maps Q to P
Check : f-¹f(x) = f-¹(3x + 5) = ⅓(3x+5) - 5/3 = x + 5/3 - 5/3 = x
Alternatively,
f(x) = 3x + 5
3x = f(x) - 5
x = ⅓f(x) - 5/3
The inverse function is : f-¹(x) = ⅓x - 5/3
Date Posted:
4 years ago
ii)
f(x) = 3x + 5
gf(x)
= 6x + 1
= 6x + 10 - 10 + 1
= 2(3x + 5) - 9
= 2f(x) - 9
Therefore, g(x) = 2x - 9
This maps Q to R.
f(x) = 3x + 5
gf(x)
= 6x + 1
= 6x + 10 - 10 + 1
= 2(3x + 5) - 9
= 2f(x) - 9
Therefore, g(x) = 2x - 9
This maps Q to R.
b)
fg(x) = 4x - 16
f(2x - 9) = 4x - 16
Recall that f(x) = 3x + 5
So f(2x - 9)
= 3(2x - 9) + 5
= 6x - 27 + 5
= 6x - 22
So 6x - 22 = 4x - 16
6x - 4x = -16 + 22
2x = 6
x = 3
fg(x) = 4x - 16
f(2x - 9) = 4x - 16
Recall that f(x) = 3x + 5
So f(2x - 9)
= 3(2x - 9) + 5
= 6x - 27 + 5
= 6x - 22
So 6x - 22 = 4x - 16
6x - 4x = -16 + 22
2x = 6
x = 3
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