Answer :
To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex], follow these steps:
1. Understand the Function:
The function is defined as [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex]. This means you multiply [tex]\(\frac{1}{7}\)[/tex] by [tex]\(7\)[/tex] raised to the power of [tex]\(x\)[/tex].
2. Substitute [tex]\(x = 3\)[/tex]:
To find [tex]\( f(3) \)[/tex], substitute 3 in place of [tex]\(x\)[/tex] in the function:
[tex]\[
f(3) = \left(\frac{1}{7}\right)\left(7^3\right)
\][/tex]
3. Calculate [tex]\(7^3\)[/tex]:
First, compute [tex]\(7^3\)[/tex]. This means multiplying 7 by itself three times:
[tex]\[
7 \times 7 \times 7 = 343
\][/tex]
4. Multiply by [tex]\(\frac{1}{7}\)[/tex]:
Next, multiply [tex]\(\frac{1}{7}\)[/tex] by the result from step 3:
[tex]\[
\frac{1}{7} \times 343 = \frac{343}{7} = 49
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is 49.
So, the correct answer is:
D. 49
1. Understand the Function:
The function is defined as [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex]. This means you multiply [tex]\(\frac{1}{7}\)[/tex] by [tex]\(7\)[/tex] raised to the power of [tex]\(x\)[/tex].
2. Substitute [tex]\(x = 3\)[/tex]:
To find [tex]\( f(3) \)[/tex], substitute 3 in place of [tex]\(x\)[/tex] in the function:
[tex]\[
f(3) = \left(\frac{1}{7}\right)\left(7^3\right)
\][/tex]
3. Calculate [tex]\(7^3\)[/tex]:
First, compute [tex]\(7^3\)[/tex]. This means multiplying 7 by itself three times:
[tex]\[
7 \times 7 \times 7 = 343
\][/tex]
4. Multiply by [tex]\(\frac{1}{7}\)[/tex]:
Next, multiply [tex]\(\frac{1}{7}\)[/tex] by the result from step 3:
[tex]\[
\frac{1}{7} \times 343 = \frac{343}{7} = 49
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is 49.
So, the correct answer is:
D. 49
