Question

I'm having a problem trying to find the inverse function of g(x) = 4(x - 3)^2 - 25.

Answer 1

I get \[g ^{-1}(x) = \frac{ 1 }{ 2 }\sqrt{x + 25} + 3\]

Answer 2

But apparently the answer is \[g ^{-1}(x) = 3 - \frac{ 1 }{ 2 }\sqrt{x + 25}\]

Answer 3

I don't understand why the answers are different?

Answer 4

this wolf pick is even better than the last nice

Answer 5

Thanks, lol

Answer 6

@hartnn

Answer 7

@Luigi0210

Answer 8

where is it mentioned that the answer is 3 -1/2 sqrt....
and NOT 3+1/2 sqrt ... ?

Answer 9

actually , when you take the square root,
you need to consider both positive and negative to get
\(\pm \sqrt{x+25}\)

so actually the final answer will be
\(g ^{-1}(x) = 3 \pm \frac{ 1 }{ 2 }\sqrt{x + 25}\)

Answer 10

Yeah, that's what I thought. But it says in the answer scheme that 3 -1/2 sqrt.... is the answer. I am busy writing a past CIE exam paper as practice for finals.

Answer 11

This was the question paper: http://papers.xtremepapers.com/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20%289709%29/9709_w12_qp_11.pdf. I'm on question 10.
Here is the mark scheme: http://papers.xtremepapers.com/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20%289709%29/9709_w12_ms_11.pdf

Answer 12

there's a domain mentioned with the answer, that was the criteria to rule out the other answer

Answer 13

Sorry, I'm having a not very bright moment. How does the domain of g^-1(x) is less than or equal to -9 rule out the one answer?

Answer 14

Is your question 10 iii in the Mark scheme doc (not sure what that means)? If so, it says x >= -9, not less than or equal.

Answer 15

Ja, the question I am working on is 10 (iii). Yes, that's right, I just looked again. My brain seems to have gone on the blink for some reason. >.<

Answer 16

personally i think the easier way for you to look at it is the g(x) is y so your problem would be y=4(x - 3)^2 - 25. so now do 4 times x and 4 times -3 then you. now set up your equation and it would be y=4x-12^2-25 so now you just switch the y and x and solve for y. so your equation would be x=4y-12^2-25 now solve for y!! hope that helped