Mathematics: Need : if h(x) = x + x^(1/2), then find h^(-1)(6).

Need : if h(x) = x + x^(1/2), then find h^(-1)(6).

Ответ:

violet9139

07.01.2022

$h(x)=x+x^{ \frac{1}{2}}
\\h=x+ \sqrt{x} 
\\x=t^2
\\h=t^2+t
$
Solve for t

$t^2+t-h=0
\\
\\t= \frac{-1\pm \sqrt{1+4h} }{2} 
\\x=t^2=(\frac{-1\pm \sqrt{1+4h} }{2} )^2$

The inverse function is

$h^{-1}(x)=(\frac{-1\pm \sqrt{1+4x} }{2} )^2$

Now find $h^{-1}(6)$

$h^{-1}(6)=(\frac{-1\pm \sqrt{1+4\times 6} }{2} )^2=(\frac{-1\pm 5 }{2} )^2
\\
\\h^{-1}(6)=4\text{ or }h^{-1}(6)=9$

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Ответ:

jholland03

31.03.2023

Mathematics

8d8sydy8sy8

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Need : if h(x) = x + x^(1/2), then find h^(-1)(6).

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