Pregunta
Suppose the functions
and
are defined as follows:
Ask by Thornton Crawford. in South Africa
Jan 23,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The solution to the equation
is
.
Solución

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Respondido por UpStudy AI y revisado por un tutor profesional
Como
Mind Expander
To solve the equation
where
, we start by substituting
into the function:
Now, isolate the square root:
To simplify, divide both sides by 2:
Next, square both sides to eliminate the square root (keeping in mind that this can potentially introduce extraneous solutions):
Now, expand the right side:
Multiply through by 4 to clear the fraction:
Expanding the square gives:
Rearranging all terms to one side:
Now we can factor the quadratic:
Setting each factor to zero gives the possible solutions:
Next, we need to check both potential solutions in the original function
to ensure they do not introduce any extraneous solutions.
For
:
For
:
Thus, the only solution to the equation
is:
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