What are sine and cosine doing here?
x → ∞ lim 3 x f − 1 ( 1 0 0 0 x ) − f − 1 ( x )
Let
f
(
x
)
=
2
7
x
3
+
(
cos
1
3
+
sin
1
3
)
x
, and let
f
−
1
(
x
)
denote the
inverse function
of
f
(
x
)
.
Compute the limit above.
The answer is 3.
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2 solutions
As x approaches ∞ the weird coefficient for the x term does matter in calculating the inverse (the awkwardness of the trig gave it away!) and so the inverse around infinity becomes just
f − 1 ( x ) = 3 3 x as x → ∞
3 x f − 1 ( 1 0 0 0 x ) − f − 1 ( x ) = 3 3 1 0 0 0 − 3 1 = 3
It's not the correct solution @Jasper Braun .
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What would make it correct, or could you post the correct one and I'll delete this?
Find the formula for f^-1 first and you will notice that the coefficient of x does not matter