Question

what is the value of $f(-1)$ for the function $f(x) = 4 \cdot 2^x$?
\\(\circ\\) a. 4
\\(\circ\\) b. 2
\\(\circ\\) c. 1
\\(\circ\\) d. 8

Explanation:

Step1: Substitute \( x = -1 \) into the function

Given \( f(x) = 4 \cdot 2^{x} \), substitute \( x=-1 \): \( f(-1)=4\cdot2^{-1} \)

Step2: Simplify the exponent

Recall \( a^{-n}=\frac{1}{a^{n}} \), so \( 2^{-1}=\frac{1}{2} \). Then \( f(-1)=4\cdot\frac{1}{2} \)

Step3: Multiply the numbers

\( 4\cdot\frac{1}{2} = 2 \)

Answer:

b. 2