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junior college 2 | H2 Maths
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Rachel
Rachel

junior college 2 chevron_right H2 Maths chevron_right Singapore

Need help for part 3! Thank you!

Date Posted: 4 years ago
Views: 361

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Wee Teck
Wee Teck's answer
59 answers (A Helpful Person)
1st
I think it is like this(?)
Rachel
Rachel
4 years ago
Yup the ans is 1! But the qn told us to solve without having to find inverse of f
Wee Teck
Wee Teck
4 years ago
I interpret it as without finding what the fxn is f^-1 is tho
Rachel
Rachel
4 years ago
Oooo ok
Rachel
Rachel
4 years ago
Im also unsure abt the 2nd to 3rd step
Eric Nicholas K
Eric Nicholas K
4 years ago
Perhaps something like

gf-1 (x) = 15
gf-1(x) f(x) = 15 f(x)
g(x) = 15 f(x)
Wee Teck
Wee Teck
4 years ago
It is just to 'undo' the adding the fxn f(x) into g(x), like how we sin^-1(sin(x)) to get x.
Rachel
Rachel
4 years ago
Ohhh ok i get it now, thanks!!!
Wee Teck
Wee Teck
4 years ago
Np, atb for ur prelim!
J
J
4 years ago
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
J
J
4 years ago
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