Question

Find inverse function of f(x) = x^2 (x in [1,4)])
please, help

Answer 1

y = x^2, solve for x then swap y and x

Answer 2

I need find :
\[f:R\0\rightarrow R\\x\rightarrow \dfrac{1}{x^2}\]
\[E=\{x \in R | 1\leq x\leq2\}\]
find \(f^{-1}(E)\)

Answer 3

so that :
let h(x) = 1/x--> h(E) =\(\{x\in R| 1\leq x\leq 2\}\) = [\(\dfrac{1}{2},1\)]

Answer 4

your R is suppose to be \( \sf \huge \mathbb{R} \)

Answer 5

and \(h^{-1}(x) = 1/x \) --> \(h^{-1}(E)=[1/2,1] \) also
but \(f^{-1}(x) = (g(h(x))^{-1}= h^{-1}(g^{-1}(x) \)

Answer 6

Yes, that is Real

Answer 7

so that I need figure out what is \(g^{-1}(E)\)

Answer 8

first off, what is g^-(x)? is it \(g^{-1}(x) = \pm \sqrt{x}\)

Answer 9

On [1,4], it's just \(\sqrt{x}\). "Function" doesn't mean much when you deliberately write "\(\pm\)"

Answer 10

correct

Answer 11

it is important that you obtain the inverse function first, then test the conditions or range of values according to parameters

Answer 12

OK, thanks for the help. :)

Answer 13

Not quite. Rephrase. It is important that you obtain the inverse RELATION first, then test the conditions or range of values according to parameters SO THAT we have a function.

There are two possible definitions for this f(x) on [1,4]. There is nothing sacred about choosing the positive one.

Words mean things. Try to use them properly.