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I think it is like this(?)
Date Posted:
4 years ago
Yup the ans is 1! But the qn told us to solve without having to find inverse of f
I interpret it as without finding what the fxn is f^-1 is tho
Oooo ok
Im also unsure abt the 2nd to 3rd step
Perhaps something like
gf-1 (x) = 15
gf-1(x) f(x) = 15 f(x)
g(x) = 15 f(x)
gf-1 (x) = 15
gf-1(x) f(x) = 15 f(x)
g(x) = 15 f(x)
It is just to 'undo' the adding the fxn f(x) into g(x), like how we sin^-1(sin(x)) to get x.
Ohhh ok i get it now, thanks!!!
Np, atb for ur prelim!
if g(x) = 15f(x)
x² - 1 = 15(x - 3)
x² - 1 = 15x - 45
x² - 15x + 44 = 0
(x - 11)(x - 4) = 0
x = 11 or x = 4
Therefore we can't apply to the function from the back, we have to do from the front.
Wee Teck's working is correct
x² - 1 = 15(x - 3)
x² - 1 = 15x - 45
x² - 15x + 44 = 0
(x - 11)(x - 4) = 0
x = 11 or x = 4
Therefore we can't apply to the function from the back, we have to do from the front.
Wee Teck's working is correct
alternate working :
gf-¹(x) = 15
(f-¹(x))² - 1 = 15
(f-¹(x))² = 16
f-¹(x) = ± 4
However, if f(x) is defined only for x ≥ 0, then f-¹(x) is only defined f-¹(x) ≥ 0 ('y' ≥ 0)
So f-¹(x) = 4
Now, the x coordinate of f maps to the y coordinate of f-¹ and the y coordinate of f maps to the x coordinate of f-¹ , since they are mirror images of each other when reflected about the line y = x.
So if f-¹(x) = 4, this means the corresponding x coordinate for f(x) is 4.
We use this to find f(x) and then map it back to the x coordinate of f-¹(x)
f(4) = 4 - 3 = 1
So for f-¹(x), the x = 1 to get f-¹(x) = 4
gf-¹(x) = 15
(f-¹(x))² - 1 = 15
(f-¹(x))² = 16
f-¹(x) = ± 4
However, if f(x) is defined only for x ≥ 0, then f-¹(x) is only defined f-¹(x) ≥ 0 ('y' ≥ 0)
So f-¹(x) = 4
Now, the x coordinate of f maps to the y coordinate of f-¹ and the y coordinate of f maps to the x coordinate of f-¹ , since they are mirror images of each other when reflected about the line y = x.
So if f-¹(x) = 4, this means the corresponding x coordinate for f(x) is 4.
We use this to find f(x) and then map it back to the x coordinate of f-¹(x)
f(4) = 4 - 3 = 1
So for f-¹(x), the x = 1 to get f-¹(x) = 4