Quiz 11.1

Question:

Find a possible formula for a power function that satisfies \(f(1)=\frac{3}{2} \) and \( f(2) = \frac{3}{8} \)

5th Ed: #13

Solution:

So the form of a power function is \( f(x) = kx^p \). We need to solve for \(k\) and \( p \) .

Using the fact that \(f (1) = \frac{3}{2} \)

\( \frac{3}{2}=k(1)^p \)
\( \frac{3}{2}=k \)

Now using the fact that \(f (2) = \frac{3}{8} \)

\( \frac{3}{8}=\frac{3}{2}(2)^p \)
\( \frac{1}{4}=2^p \)
\( p=-2 \)

Therefore \(f(x)=\frac{3}{2} x^{-2} \)