Final answer:
To find (f g)(x), substitute g(x) in place of x in f(x) equation and simplify the expression. To find (f g)(4), substitute x = 4 in (f g)(x) equation and simplify the expression.
Step-by-step explanation:
To find (f g)(x), we need to perform the composition of functions. The composition of two functions f and g is denoted as (f g)(x) and is obtained by substituting the output of g into f. In this case, f(x) = 4x² - x - 5 and g(x) = x - 1.
So, (f g)(x) = f(g(x)).
Substituting g(x) in place of x in f(x), we get (f g)(x) = f(x - 1).
Expanding f(x - 1), we get (f g)(x) = 4(x - 1)² - (x - 1) - 5.
Simplifying further, (f g)(x) = 4(x² - 2x + 1) - x + 1 - 5.
Combining like terms, (f g)(x) = 4x² - 8x + 4 - x - 4 - 5.
Finally, (f g)(x) = 4x² - 9x - 5.
To find (f g)(4), we can substitute x = 4 in (f g)(x) equation.
So, (f g)(4) = 4(4)² - 9(4) - 5.
Simplifying further, (f g)(4) = 4(16) - 36 - 5.
(f g)(4) = 64 - 36 - 5.
Therefore, (f g)(4) = 23.