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Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Stuck on a part of a question (integration topic)

Hi all,

Attached is an image of the question, i'm stuck on part iv) have no idea how I can go about it really. Any help would be appreciated!

OP

Damn it, the picture is too small.

Basically if f(x) is 4x(2x-1)^7 anf f(1) = 4

then what is d/dx(f^-1(x)) when x = 4

The derivative at the point

x = a

is given by

\displaystyle \frac{df^{-1}}{dx} = \frac{1}{\displaystyle \frac{df}{dx}}

where you evaluate

\displaystyle \frac{df}{dx}

at the point

x = f^{-1}(a)

.

OP

Original post by jack.hadamard

The derivative at the point

x = a

is given by

\displaystyle \frac{df^{-1}}{dx} = \frac{1}{\displaystyle \frac{df}{dx}}

where you evaluate

\displaystyle \frac{df}{dx}

at the point

x = f^{-1}(a)

.

So do I work out the inverse of 4x(2x-1)^7? that seems way too complicated?

Original post by Robskeh

So do I work out the inverse of 4x(2x-1)^7?

Derivative. After that, you need to use

f^{-1}(4)

.

Original post by Robskeh

Hi all,

Attached is an image of the question, i'm stuck on part iv) have no idea how I can go about it really. Any help would be appreciated!

Where does the question come from, I have not seen one like this on any C4 paper?

I found this helpful http://archives.math.utk.edu/visual.calculus/3/inverse.1/index.html

So my solution is:

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