O Graphs and Functions Variable expressions as inputs of functions: Problem type 2 The function \( f \) is defined as \( f(x)=\frac{-8}{4 x^{2}+5} \). Find \( f(x-3) \). Write your answer without parentheses, and simplify it as much as possible. \( f(x-3)=\square \)

To find \( f(x-3) \), we substitute \( x-3 \) into the function \( f(x) \). Given \( f(x) = \frac{-8}{4x^2 + 5} \), we replace \( x \) with \( x-3 \): \[ f(x-3) = \frac{-8}{4(x-3)^2 + 5} \] Next, we need to simplify \( (x-3)^2 \): \[ (x-3)^2 = x^2 - 6x + 9 \] Now, substituting this back in gives us: \[ f(x-3) = \frac{-8}{4(x^2 - 6x + 9) + 5} \] Now distribute the 4: \[ = \frac{-8}{4x^2 - 24x + 36 + 5} \] \[ = \frac{-8}{4x^2 - 24x + 41} \] Therefore, the final answer is: \[ f(x-3) = \frac{-8}{4x^2 - 24x + 41} \]