Playing with Graphs --- 5
f ( x ) = 8 x 2 + 1 2 x − 1 7 − 4 9 + 8 x
Find the root of the equation above, for x ∈ [ − 4 3 , ∞ )
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The answer is 1.158.
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2 solutions
It is brilliant! . My Approach was different but i did not landed at exact answer i only estimated a range of x using graphical approach but this is nice ! upvoted bro :)
So u got me right
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This answer is incorrect. Plug. 1.158 back into the equation. You will see that it is wrong.
we use Geogebra :)
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What is that??? I will like to know , please can tu write yr solution :)
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You can say Geogebra is a "cheating method" to solve the question.
Why would you subtract x from the discriminant?
Is it always true that the solution of f(x) and f^(-1)(x) lies on y= x? @Md Zuhair @Thomas Jacob @Aaron Jerry Ninan @Rahil Sehgal
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Yeah, If a solution exists, then it will be definitely on y=x.
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It is not always the case , a graph when reflected about y=x may lead to some intersection points not lying on y=x.
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@Ankit Kumar Jain – Yes, take for instance y= -x+sinx
HINT : If you check carefully , you will see that the equation is of the form F ( x ) = F − 1 ( x )
Seriously LEGENDARY question! Troubled me for over a week!
how did you come to this conclusion?
As, Aniket told, the question is of form f − 1 ( x ) = f ( x ) so we just have to figure out the function. Clearly by common sense function will be quadratic.
So let f ( x ) = a x 2 + b x + c
So our given equation if of form:
a x 2 + b x + c = 2 a − b + b 2 − 4 a ( c − x )
⇒ 2 a 2 x 2 + 2 b a x + 2 a c + b = b 2 − 4 a ( c − x )
Comparing coefficients, we get a = 2 , b = 3 , c = − 5
Now as f − 1 ( x ) = f ( x ) so its root will lie on the line y = x or precisely
2 x 2 + 3 x − 5 = x
Solving for x we get x = 1 . 1 5 8