What is the answer for question 7. a) ?

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Given `f(x)=2(x-4)^2+5`

fraph of this function is

Let Inverse of f i.e `f^(-1)(x)` ,where

either

`f^(-1)(x)=4-sqrt((x-5)/2)` or

or

`f^(-1)(x)=4+sqrt((x-5)/2)`

But `f^(-1)(x)!=4+-sqrt((x-5)/2)` otherwise it can not be function.

Its domain be all real numbers `x>=5` .

Its graph `f^(-1)(x)=4-sqrt((x-5)/2)`

and

graph for

`f^(-1)(x)=4+sqrt((x-5)/2)`

But the graph of

`f^(-1)(x)=4+-sqrt((x-5)/2)`

Thus for one value of x , we are getting two values of `f^(-1)(x).`

So this is not possible for function.

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