Answer :
To find the value of the function [tex]\( f(x) = 3 \cdot 25^x \)[/tex] at [tex]\( x = \frac{1}{2} \)[/tex], we'll substitute [tex]\(\frac{1}{2}\)[/tex] into the function and simplify.
Here's the step-by-step solution:
1. Start with the function:
[tex]\[
f(x) = 3 \cdot 25^x
\][/tex]
2. Substitute [tex]\( x = \frac{1}{2} \)[/tex] into the function:
[tex]\[
f\left(\frac{1}{2}\right) = 3 \cdot 25^{\frac{1}{2}}
\][/tex]
3. Note that raising a number to the power of [tex]\(\frac{1}{2}\)[/tex] is equivalent to taking the square root of that number. Therefore, [tex]\( 25^{\frac{1}{2}} = \sqrt{25} \)[/tex].
4. Calculate the square root of 25:
[tex]\[
\sqrt{25} = 5
\][/tex]
5. Substitute back to find the function value:
[tex]\[
f\left(\frac{1}{2}\right) = 3 \cdot 5
\][/tex]
6. Multiply 3 by 5:
[tex]\[
f\left(\frac{1}{2}\right) = 15
\][/tex]
So, the value of [tex]\( f\left(\frac{1}{2}\right) \)[/tex] is 15.
Here's the step-by-step solution:
1. Start with the function:
[tex]\[
f(x) = 3 \cdot 25^x
\][/tex]
2. Substitute [tex]\( x = \frac{1}{2} \)[/tex] into the function:
[tex]\[
f\left(\frac{1}{2}\right) = 3 \cdot 25^{\frac{1}{2}}
\][/tex]
3. Note that raising a number to the power of [tex]\(\frac{1}{2}\)[/tex] is equivalent to taking the square root of that number. Therefore, [tex]\( 25^{\frac{1}{2}} = \sqrt{25} \)[/tex].
4. Calculate the square root of 25:
[tex]\[
\sqrt{25} = 5
\][/tex]
5. Substitute back to find the function value:
[tex]\[
f\left(\frac{1}{2}\right) = 3 \cdot 5
\][/tex]
6. Multiply 3 by 5:
[tex]\[
f\left(\frac{1}{2}\right) = 15
\][/tex]
So, the value of [tex]\( f\left(\frac{1}{2}\right) \)[/tex] is 15.
