For the given functions f and g, find the requested composite function.
-$f ( x ) = x ^ { 2 } - 5 , \quad g ( x ) = x ^ { 2 } - 8 ; \quad$ Find $( f \circ g ) ( x )$
A) $x ^ { 4 } - 16 x ^ { 2 } + 59$
B) $x ^ { 4 } + 17$
C) $x ^ { 4 } + 59$
D) $x ^ { 4 } - 10 x ^ { 2 } + 17$

Question

Quizplus · Accepted Answer

To find $ ( f \circ g ) ( x ) $, we replace $ x $ in $ f ( x ) $ with $ g ( x ) $:$$( f \circ g ) ( x ) = f ( g ( x ) ) = f ( x ^ { 2 } - 8 ) = ( x ^ { 2 } - 8 ) ^ { 2 } - 5 = x ^ { 4 } - 16 x ^ { 2 } + 59$$

For the Given Functions F and G, Find the Requested f(x)=x2−5,g(x)=x2−8;f ( x ) = x ^ { 2 } - 5 , \quad g ( x ) = x ^ { 2 } - 8 ; \quadf(x)=x2−5,g(x)=x2−8;

For the Given Functions F and G, Find the Requested $f ( x ) = x ^ { 2 } - 5 , \quad g ( x ) = x ^ { 2 } - 8 ; \quad$