anonymous
  • anonymous
Determine the inverse function (Calculus 1 Homework)
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
determine the inverse function \[f ^{-1}\] of f when \[f(x)=\sqrt{3+7x}\] \[x \ge \frac{ -3 }{ 7 }\]
Mimi_x3
  • Mimi_x3
\[ y = \sqrt{3+7x}\] \[ x = \sqrt{ 3+ 7y}\] \[ \sqrt{3+7y} = x\] \[ 3+ 7y = x^2\] \[ 7y = x^2 - 3\] \[ y = \frac{x^2-3}{7}\]
anonymous
  • anonymous
@Mimi_x3 then it also says the answer is \[x \ge0\]

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anonymous
  • anonymous
why?
Mimi_x3
  • Mimi_x3
maybe cos of the condition?
zzr0ck3r
  • zzr0ck3r
think of y = x^2 y = sqrt(x) is the inverse if we restrict x >= 0
zzr0ck3r
  • zzr0ck3r
its only an inverse for x>=0 because we lose the negative if we make x negative f(f^(-1)(x)) = x for all x is a must and this is not the case unless we restrict the domain. this happens when we try and find the inverse of even roots
zzr0ck3r
  • zzr0ck3r
the problem is here @Mimi_x3 \[\sqrt{3+7y}=x\\\text{this implies that }x\ge0\\\text{we loose that information in your next step}\\3+7y = x^2\]
DebbieG
  • DebbieG
Another way to think of the restriction on the domain of the inverse is to simply think about the range of the original function. If you know what the range of \(f(x)=\sqrt{3+7x}\) is (can you picture the graph?... this is just a transformation on \(f(x)=\sqrt{x}\)), then you know that the domain of f(x) is \(x\ge0\), so the range of the inverse must be \(y\ge0\). The inverse of a function has the DOMAIN of the original for its RANGE, and the RANGE OF of the original for its DOMAIN. That's what the inverse does, after all - it "flips" the funcion's domain and range values. :)
zzr0ck3r
  • zzr0ck3r
correct:)
zzr0ck3r
  • zzr0ck3r
so really asking for inverse without stating domain and co-domain is sort of pointless, we just assume that both are R
dan815
  • dan815
i wanna be GREEN

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