Question

Suppose that the functions p and g are defined as follows,p(x) = x² +7g(x)=√x+4Find the following,(gp) (5)=X(pog)(5) =5?

Answer 1

Answer:

(gp) (5)= sqrt(32)+4

(pog)(5) = 28+8sqrt(5)

Step-by-step explanation:

We are given the following functions:

$p(x)=x^2+7,g(x)=\sqrt{x}+4$

(gp) (5)=

(gp) means that the outside function is g and the inside is p:

So

$g\circ p(x)=g(x^2+7)=\sqrt{x^2+7}+4$

At x = 5

$(g\circ p)(5)=\sqrt{5^2+7}+4=\sqrt{32}+4$

(gp) (5)= sqrt(32)+4

(pog)(5) =

Outside p, inside g. So

$(p\circ g)(x)=p(\sqrt{x}+4)=(\sqrt{x}+4)^2+7=(\sqrt{x})^2+8\sqrt{x}+16+7=x+8\sqrt{x}+23$

At x = 5

$(p\circ g)(5)=5+8\sqrt{5}+23=28+8\sqrt{5}$

(pog)(5) = 28+8sqrt(5)