We're glad you stopped by Given tex f x 5 2x tex evaluate tex f 1 f 0 tex and tex f 2 tex A tex frac 1 25 1. This page is here to walk you through essential details with clear and straightforward explanations. Our goal is to make your learning experience easy, enriching, and enjoyable. Start exploring and find the information you need!
Answer :
To evaluate the function [tex]\(f(x) = 5^{2x}\)[/tex] at [tex]\(x = -1\)[/tex], [tex]\(x = 0\)[/tex], and [tex]\(x = 2\)[/tex], we'll substitute these values into the equation one by one:
1. Evaluate [tex]\(f(-1)\)[/tex]:
Substitute [tex]\(-1\)[/tex] into the function:
[tex]\[
f(-1) = 5^{2 \times (-1)} = 5^{-2}
\][/tex]
The expression [tex]\(5^{-2}\)[/tex] means [tex]\(\frac{1}{5^2}\)[/tex], which is [tex]\(\frac{1}{25}\)[/tex].
2. Evaluate [tex]\(f(0)\)[/tex]:
Substitute [tex]\(0\)[/tex] into the function:
[tex]\[
f(0) = 5^{2 \times 0} = 5^0
\][/tex]
We know that any non-zero number raised to the power of 0 is 1. So, [tex]\(f(0) = 1\)[/tex].
3. Evaluate [tex]\(f(2)\)[/tex]:
Substitute [tex]\(2\)[/tex] into the function:
[tex]\[
f(2) = 5^{2 \times 2} = 5^4
\][/tex]
Calculate [tex]\(5^4\)[/tex]:
[tex]\[
5^4 = 5 \times 5 \times 5 \times 5 = 625
\][/tex]
Based on these calculations, the results are [tex]\(f(-1) = \frac{1}{25}\)[/tex], [tex]\(f(0) = 1\)[/tex], and [tex]\(f(2) = 625\)[/tex].
Therefore, the correct option that matches these values is:
[tex]\(\frac{1}{25}, 1, 625\)[/tex].
1. Evaluate [tex]\(f(-1)\)[/tex]:
Substitute [tex]\(-1\)[/tex] into the function:
[tex]\[
f(-1) = 5^{2 \times (-1)} = 5^{-2}
\][/tex]
The expression [tex]\(5^{-2}\)[/tex] means [tex]\(\frac{1}{5^2}\)[/tex], which is [tex]\(\frac{1}{25}\)[/tex].
2. Evaluate [tex]\(f(0)\)[/tex]:
Substitute [tex]\(0\)[/tex] into the function:
[tex]\[
f(0) = 5^{2 \times 0} = 5^0
\][/tex]
We know that any non-zero number raised to the power of 0 is 1. So, [tex]\(f(0) = 1\)[/tex].
3. Evaluate [tex]\(f(2)\)[/tex]:
Substitute [tex]\(2\)[/tex] into the function:
[tex]\[
f(2) = 5^{2 \times 2} = 5^4
\][/tex]
Calculate [tex]\(5^4\)[/tex]:
[tex]\[
5^4 = 5 \times 5 \times 5 \times 5 = 625
\][/tex]
Based on these calculations, the results are [tex]\(f(-1) = \frac{1}{25}\)[/tex], [tex]\(f(0) = 1\)[/tex], and [tex]\(f(2) = 625\)[/tex].
Therefore, the correct option that matches these values is:
[tex]\(\frac{1}{25}, 1, 625\)[/tex].
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