Questions: Choose f(g(x)). Given: f(x)=x^2/2 ; g(x)=x+2 3x^2+2 x^2+2x+2 x^2/2+2 (x^2+4x+4)/2

Solution Steps

To find \( f(g(x)) \), we need to substitute \( g(x) \) into \( f(x) \). Given \( f(x) = \frac{x^2}{2} \) and \( g(x) = x + 2 \), we substitute \( x + 2 \) for \( x \) in \( f(x) \).

We are given two functions:

• \( f(x) = \frac{x^2}{2} \)
• \( g(x) = x + 2 \)

To find \( f(g(x)) \), we substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(x + 2) = \frac{(x + 2)^2}{2} \]

Next, we expand \( (x + 2)^2 \): \[ (x + 2)^2 = x^2 + 4x + 4 \] Thus, \[ f(g(x)) = \frac{x^2 + 4x + 4}{2} \]

Now, we evaluate \( f(g(1)) \): \[ g(1) = 1 + 2 = 3 \] Then, \[ f(g(1)) = f(3) = \frac{3^2}{2} = \frac{9}{2} = 4.5 \]

Final Answer