Select Function Set \( 3, f(x)=x^{2} \) and \( g(x)=\sqrt{x+3} \), and check both Display \( (f \circ g)(x) \) and \( (g \circ f)(x) \) boxes. Is it true or false that the function \( (f \circ g)(x) \) is equivalent to \( (g \circ f)(x) \) ? Use the interactive figure to find your answer. Use the left and right arrow keys to move along a slider as needed. Click here to launch the interactive figure. Choose the correct answer below. True False

To determine if \( (f \circ g)(x) \) is equivalent to \( (g \circ f)(x) \), we need to evaluate both compositions: 1. **For \( (f \circ g)(x) \)**: This means you first apply \( g(x) \) and then \( f(x) \). So, \[ (f \circ g)(x) = f(g(x)) = f(\sqrt{x+3}) = (\sqrt{x+3})^2 = x + 3 \] 2. **For \( (g \circ f)(x) \)**: Here, you first apply \( f(x) \) and then \( g(x) \). So, \[ (g \circ f)(x) = g(f(x)) = g(x^2) = \sqrt{x^2 + 3} \] Now comparing the two results: - \( (f \circ g)(x) = x + 3 \) - \( (g \circ f)(x) = \sqrt{x^2 + 3} \) Since \( x + 3 \) is not equal to \( \sqrt{x^2 + 3} \) for all values of \( x \), it is **False** that \( (f \circ g)(x) \) is equivalent to \( (g \circ f)(x) \).