Question: The function \( g \) is defined by \( g(x) = x^2 - 4 \). Find \( g(5x) \). \( g(5x) =…

The function \( g \) is defined by \( g(x) = x^2 - 4 \).

Find \( g(5x) \).

\( g(5x) = \boxed{\phantom{0}} \)

Solution

The function \( g \) is defined by \( g(x) = x^2 - 4 \). To find \( g(5x) \), substitute \( 5x \) into the function in place of \( x \). Start with the original function: \[ g(x) = x^2 - 4 \] Substitute \( 5x \) for \( x \): \[ g(5x) = (5x)^2 - 4 \] Calculate \( (5x)^2 \): \[ g(5x) = 25x^2 - 4 \] Thus, \( g(5x) = 25x^2 - 4 \).