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. Substitute [tex]\( x = 3 \)[/tex] into the function:
We need to find [tex]\( f(3) \)[/tex], so substitute 3 into the function:
[tex]\[
f(3) = \left(\frac{1}{7}\right)\left(7^3\right)
\][/tex]
2. Calculate [tex]\( 7^3 \)[/tex]:
Next, compute the value of [tex]\( 7^3 \)[/tex]:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
3. Multiply by [tex]\( \frac{1}{7} \)[/tex]:
Now, multiply the result by [tex]\( \frac{1}{7} \)[/tex]:
[tex]\[
f(3) = \frac{1}{7} \times 343
\][/tex]
4. Perform the multiplication:
To multiply, divide 343 by 7:
[tex]\[
\frac{343}{7} = 49
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is 49. Hence, the correct answer is:
A. 49
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
We need to find [tex]\( f(3) \)[/tex], so substitute 3 into the function:
[tex]\[
f(3) = \left(\frac{1}{7}\right)\left(7^3\right)
\][/tex]
2. Calculate [tex]\( 7^3 \)[/tex]:
Next, compute the value of [tex]\( 7^3 \)[/tex]:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
3. Multiply by [tex]\( \frac{1}{7} \)[/tex]:
Now, multiply the result by [tex]\( \frac{1}{7} \)[/tex]:
[tex]\[
f(3) = \frac{1}{7} \times 343
\][/tex]
4. Perform the multiplication:
To multiply, divide 343 by 7:
[tex]\[
\frac{343}{7} = 49
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is 49. Hence, the correct answer is:
A. 49
