for ( f(x)=x + 3 ) and ( g(x)=5x + 5 ), find the following functions.\na. ( (fcirc g)(x) ); b. ( (gcirc…

for ( f(x)=x + 3 ) and ( g(x)=5x + 5 ), find the following functions.\na. ( (fcirc g)(x) ); b. ( (gcirc f)(x) ); c. ( (fcirc g)(-2) ); d. ( (gcirc f)(-2) )\na. ( (fcirc g)(x)=square ) (simplify your answer.)

for ( f(x)=x + 3 ) and ( g(x)=5x + 5 ), find the following functions.\na. ( (fcirc g)(x) ); b. ( (gcirc f)(x) ); c. ( (fcirc g)(-2) ); d. ( (gcirc f)(-2) )\na. ( (fcirc g)(x)=square ) (simplify your answer.)

Answer

Explanation:

Step1: Recall the composition formula

The composition of functions ((f\circ g)(x)=f(g(x))). Given (f(x)=x + 3) and (g(x)=5x+5). Substitute (g(x)) into (f(x)): (f(g(x))=(5x + 5)+3).

Step2: Simplify the expression

Combine like - terms: ((5x+5)+3=5x+(5 + 3)=5x+8).

Answer:

(5x + 8)