Find (a) \( f(g(x)),(\mathrm{b}) g(f(x)) \), and \( (\mathrm{c}) f(f(x)) \) \( f(x)=-5 x, g(x)=x+6 \) a. \( f(g(x))=\square \) b. \( g(f(x))=\square \) c. \( f(f(x))=\square \)

To find (a) \( f(g(x)) \), (b) \( g(f(x)) \), and (c) \( f(f(x)) \) for the functions \( f(x) = -5x \) and \( g(x) = x + 6 \): a. To find \( f(g(x)) \): \[ g(x) = x + 6 \] Now, plug \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(x + 6) = -5(x + 6) = -5x - 30 \] So, \( f(g(x)) = -5x - 30 \). b. To find \( g(f(x)) \): \[ f(x) = -5x \] Now, plug \( f(x) \) into \( g(x) \): \[ g(f(x)) = g(-5x) = -5x + 6 \] So, \( g(f(x)) = -5x + 6 \). c. To find \( f(f(x)) \): \[ f(x) = -5x \] Now, plug \( f(x) \) into itself: \[ f(f(x)) = f(-5x) = -5(-5x) = 25x \] So, \( f(f(x)) = 25x \). Thus, the final answers are: a. \( f(g(x)) = -5x - 30 \) b. \( g(f(x)) = -5x + 6 \) c. \( f(f(x)) = 25x \)