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Given #f(x)= x^3 +2x -1#, how do you find #1/ [f^(-1)(2)]#?

Answer 1

Charles Anctil

#1/f^(-1)(2) = 1#

If #f(x) = 2# then we have:

#x^3+2x-1 = 2#

and so:

#0 = x^3+2x-3 = (x-1)(x^2+x+3) = (x-1)((x+1/2)^2+11/4)#

So the only Real root is #x = 1# and we find:

#1/f^(-1)(2) = 1/1 = 1#

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Answer 2

Luke Alvarez

To find ( \frac{1}{f^{-1}(2)} ), follow these steps:

Determine the inverse function of ( f(x) ), denoted as ( f^{-1}(x) ).
Once you find ( f^{-1}(x) ), evaluate ( f^{-1}(2) ).
Then, calculate ( \frac{1}{f^{-1}(2)} ).

Here's the detailed process:

Start with the given function: ( f(x) = x^3 + 2x - 1 ).
To find the inverse function ( f^{-1}(x) ), swap ( x ) and ( y ) in the equation and solve for ( y ).
So, ( x = y^3 + 2y - 1 ).
Rearrange this equation to solve for ( y ).
Once you find ( f^{-1}(x) ), plug in ( x = 2 ) to find ( f^{-1}(2) ).
Finally, calculate ( \frac{1}{f^{-1}(2)} ).

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Answer 3

William Abdalla

To find (\frac{1}{f^{-1}(2)}), first find the inverse function of (f(x) = x^3 + 2x - 1), denoted as (f^{-1}(x)). Then, substitute (2) into the inverse function and take the reciprocal of the result.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.