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], we can follow these steps:
1. Identify the Function: The function is given by [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex].
2. Substitute the Value of [tex]\( x \)[/tex]: We need to find [tex]\( f(3) \)[/tex], so we substitute [tex]\( x = 3 \)[/tex] into 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]\[
7^3 = 7 \times 7 \times 7 = 49 \times 7 = 343
\][/tex]
4. Multiply by [tex]\(\frac{1}{7}\)[/tex]: Now, multiply the result by [tex]\(\frac{1}{7}\)[/tex]:
[tex]\[
\left(\frac{1}{7}\right) \times 343 = \frac{343}{7}
\][/tex]
5. Simplify the Fraction: Finally, divide 343 by 7:
[tex]\[
\frac{343}{7} = 49
\][/tex]
6. Conclusion: The value of [tex]\( f(3) \)[/tex] is 49. Thus, the correct answer is [tex]\(\boxed{49}\)[/tex].
1. Identify the Function: The function is given by [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex].
2. Substitute the Value of [tex]\( x \)[/tex]: We need to find [tex]\( f(3) \)[/tex], so we substitute [tex]\( x = 3 \)[/tex] into 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]\[
7^3 = 7 \times 7 \times 7 = 49 \times 7 = 343
\][/tex]
4. Multiply by [tex]\(\frac{1}{7}\)[/tex]: Now, multiply the result by [tex]\(\frac{1}{7}\)[/tex]:
[tex]\[
\left(\frac{1}{7}\right) \times 343 = \frac{343}{7}
\][/tex]
5. Simplify the Fraction: Finally, divide 343 by 7:
[tex]\[
\frac{343}{7} = 49
\][/tex]
6. Conclusion: The value of [tex]\( f(3) \)[/tex] is 49. Thus, the correct answer is [tex]\(\boxed{49}\)[/tex].
