For the following function, find \( f(2.1) \) and \( f(4) \). \( f(x)=\left\{\begin{array}{ll}2 x-3, & 0

Ask by Vega Carlson. in the United States

Jan 02,2025

To find \( f(2.1) \) and \( f(4) \), we need to look at the piecewise function given. For \( x = 2.1 \): Since \( 2 < x < 4 \), we use the second piece of the function: \( f(x) = \frac{1}{2}x^2 \). Calculating \( f(2.1) \): \[ f(2.1) = \frac{1}{2}(2.1)^2 = \frac{1}{2}(4.41) = 2.205 \] For \( x = 4 \): Since \( 4 \leq x < 8 \), we use the third piece of the function: \( f(x) = \log_2 x \). Calculating \( f(4) \): \[ f(4) = \log_2(4) = 2 \] So, \( f(2.1) = 2.205 \) and \( f(4) = 2 \). The correct answer is: \( f(2.1) = 2.205 \) and \( f(4) = 2 \).