Answer :
To solve the problem of finding [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 given as [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex]. This means you first raise 7 to the power of [tex]\( x \)[/tex], and then multiply the result by [tex]\(\frac{1}{7}\)[/tex].
2. Substitute [tex]\( x = 3 \)[/tex]: Replace [tex]\( x \)[/tex] with 3 in the function:
[tex]\[
f(3) = \left(\frac{1}{7}\right)\left(7^3\right)
\][/tex]
3. Calculate [tex]\( 7^3 \)[/tex]:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
4. Multiply by [tex]\(\frac{1}{7}\)[/tex]:
[tex]\[
f(3) = \frac{1}{7} \times 343
\][/tex]
5. Simplify the Multiplication:
[tex]\[
\frac{1}{7} \times 343 = \frac{343}{7}
\][/tex]
6. Divide 343 by 7:
[tex]\[
343 \div 7 = 49
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is 49.
The correct answer is:
D. 49
1. Understand the Function: The function is given as [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex]. This means you first raise 7 to the power of [tex]\( x \)[/tex], and then multiply the result by [tex]\(\frac{1}{7}\)[/tex].
2. Substitute [tex]\( x = 3 \)[/tex]: Replace [tex]\( x \)[/tex] with 3 in the function:
[tex]\[
f(3) = \left(\frac{1}{7}\right)\left(7^3\right)
\][/tex]
3. Calculate [tex]\( 7^3 \)[/tex]:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
4. Multiply by [tex]\(\frac{1}{7}\)[/tex]:
[tex]\[
f(3) = \frac{1}{7} \times 343
\][/tex]
5. Simplify the Multiplication:
[tex]\[
\frac{1}{7} \times 343 = \frac{343}{7}
\][/tex]
6. Divide 343 by 7:
[tex]\[
343 \div 7 = 49
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is 49.
The correct answer is:
D. 49
