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 follow these steps:
1. Identify the given function: [tex]\( f(x) = \left(\frac{1}{7}\right) \left(7^x\right) \)[/tex].
2. Substitute the value of [tex]\( x \)[/tex] with 3: You want to find [tex]\( f(3) \)[/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 the exponent: First, calculate [tex]\( 7^3 \)[/tex]:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343.
\][/tex]
4. Multiply by [tex]\(\frac{1}{7}\)[/tex]: Now multiply the result of the exponentiation by [tex]\(\frac{1}{7}\)[/tex]:
[tex]\[
f(3) = \left(\frac{1}{7}\right) \times 343 = \frac{343}{7}.
\][/tex]
5. Simplify the fraction: Divide 343 by 7:
[tex]\[
\frac{343}{7} = 49.
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is 49. The answer is [tex]\(\boxed{49}\)[/tex].
1. Identify the given function: [tex]\( f(x) = \left(\frac{1}{7}\right) \left(7^x\right) \)[/tex].
2. Substitute the value of [tex]\( x \)[/tex] with 3: You want to find [tex]\( f(3) \)[/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 the exponent: First, calculate [tex]\( 7^3 \)[/tex]:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343.
\][/tex]
4. Multiply by [tex]\(\frac{1}{7}\)[/tex]: Now multiply the result of the exponentiation by [tex]\(\frac{1}{7}\)[/tex]:
[tex]\[
f(3) = \left(\frac{1}{7}\right) \times 343 = \frac{343}{7}.
\][/tex]
5. Simplify the fraction: Divide 343 by 7:
[tex]\[
\frac{343}{7} = 49.
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is 49. The answer is [tex]\(\boxed{49}\)[/tex].
