Express the given function as a composite of functions f and g such that y = f(g(x)).
-$y = ( 8 x - 19 ) ^ { 4 }$
A) $f ( x ) = ( 8 x ) ^ { 4 } , g ( x ) = - 19$
B) $f ( x ) = 8 x - 19 , g ( x ) = x ^ { 4 }$
C) $f ( x ) = x ^ { 4 } , g ( x ) = 8 x - 19$
D) $f ( x ) = 8 x ^ { 4 } , g ( x ) = x - 19$

Question

Quizplus · Accepted Answer

We can express the given function as a composite of functions f and g only if we can break it down into two parts: an inner function g that takes an input x and produces an intermediate result, and an outer function f that takes this intermediate result and produces the final output y. Looking at the given function, we can rewrite it as follows:

$y = ( 8 x - 19 ) ^ { 4 } = ( g ( x ) ) ^ { 4 } = f ( g ( x ) )$

where g ( x ) = 8 x - 19 and f ( x ) = x ^ { 4 }. Therefore, the best choice is C, with g ( x ) = 8 x - 19 and f ( x ) = x ^ { 4 }.

Express the Given Function as a Composite of Functions F y=(8x−19)4y = ( 8 x - 19 ) ^ { 4 }y=(8x−19)4

Express the Given Function as a Composite of Functions F $y = ( 8 x - 19 ) ^ { 4 }$