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Answer :
Answer:
C
Step-by-step explanation:
Assuming the function is
f(x) = 3 • [tex]25^{x}[/tex]
Then using the property of exponents/ radicals
• [tex]a^{\frac{1}{2} }[/tex] = [tex]\sqrt{a}[/tex]
To evaluate f( [tex]\frac{1}{2}[/tex] ) , substitute x = [tex]\frac{1}{2}[/tex] into f(x) , that is
f( [tex]\frac{1}{2}[/tex] )
= 3 × [tex]25^{\frac{1}{2} }[/tex]
= 3 × [tex]\sqrt{25}[/tex]
= 3 × 5
= 15
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Rewritten by : Barada
To find the value of the function given by [tex]f(x) = 3 \cdot 25^{x^{1/2}}[/tex] at [tex]x = \frac{1}{2}[/tex], we first need to substitute [tex]\frac{1}{2}[/tex] into the function.
Calculate [tex]f\left(\frac{1}{2}\right)[/tex]:
[tex]f\left(\frac{1}{2}\right) = 3 \cdot 25^{\left(\frac{1}{2}\right)^{1/2}}[/tex]
Since [tex]\left(\frac{1}{2}\right)^{1/2} = \sqrt{\frac{1}{2}} = \frac{1}{\sqrt{2}}[/tex], we can rewrite it as:
[tex]f\left(\frac{1}{2}\right) = 3 \cdot 25^{\frac{1}{\sqrt{2}}}[/tex]Calculate [tex]25^{\frac{1}{\sqrt{2}}}[/tex]:
We recognize that [tex]25 = 5^2[/tex], thus:
[tex]25^{\frac{1}{\sqrt{2}}} = (5^2)^{\frac{1}{\sqrt{2}}} = 5^{\frac{2}{\sqrt{2}}} = 5^{\sqrt{2}}[/tex]
This means our function becomes:
[tex]f\left(\frac{1}{2}\right) = 3 \cdot 5^{\sqrt{2}}[/tex]Now, we will consider the subtraction specified in the question:
[tex]f\left(\frac{1}{2}\right) - 40[/tex]We need to calculate the approximate value of [tex]5^{\sqrt{2}}[/tex]:
Since [tex]\sqrt{2}[/tex] is approximately [tex]1.414[/tex], we can estimate:
[tex]5^{\sqrt{2}} \approx 5^{1.414} \approx 6.9 \text{ (using a scientific calculator or logarithm)}[/tex]
Therefore, we can substitute this value into the function:
[tex]f\left(\frac{1}{2}\right) \approx 3 \cdot 6.9 \approx 20.7[/tex]Now performing the subtraction:
[tex]20.7 - 40 \approx -19.3[/tex]
From analyzing the values the question provided later (-150, -15, -225), the subtraction is simplified to finding how [tex]-19.3[/tex] would compare to these other values in magnitude.
In conclusion, we have:
- The function value at [tex]x = \frac{1}{2}[/tex] is approximately [tex]20.7[/tex].
- The result of [tex]f\left(\frac{1}{2}\right) - 40[/tex] is approximately [tex]-19.3[/tex].
Therefore, if you want to understand or perform further calculations, you may adjust these values based on the needs presented in your question.
