If \( f(x)=2 x^{2}+5 \) and \( g(x)=x^{2}-2 \), find \( (f-g)(x) \)

To find \( (f-g)(x) \), we need to subtract the function \( g(x) \) from \( f(x) \). We start with the functions: \[ f(x) = 2x^{2} + 5 \] \[ g(x) = x^{2} - 2 \] Now, we can calculate \( (f-g)(x) \): \[ (f-g)(x) = f(x) - g(x) = (2x^{2} + 5) - (x^{2} - 2) \] Distributing the negative sign: \[ (f-g)(x) = 2x^{2} + 5 - x^{2} + 2 \] Now, combine like terms: \[ (f-g)(x) = (2x^{2} - x^{2}) + (5 + 2) = x^{2} + 7 \] Thus, the result is: \[ (f-g)(x) = x^{2} + 7 \]