Respuesta :

[tex]\bf \begin{cases} f(x)=2x\\ g(x)=2x-1\\ h(x)=\sqrt{x} \end{cases}\qquad \begin{array}{llll} (f\circ g\circ h)(x)\\ (f[g\circ h])(x)\\ (\ f[\ g(\ h(x)\ )\ ]\ ) \end{array}\\\\ -----------------------------\\\\ g(\ h(x)\ )=2[h(x)]-1\implies 2\sqrt{x}-1 \\\\\\ f[\ g(\ h(x)\ )\ ]=2[\ g(\ h(x)\ )\ ]\implies 2(2\sqrt{x}-1) \\\\\\ f[\ g(\ h(\quad 9\quad )\ )\ ]=2(2\sqrt{9}-1)\implies 4\sqrt{9}-1\implies 4\cdot 3-1\implies 11[/tex]

Answer:

10

Step-by-step explanation:

[tex]f(x)= 2x[/tex], [tex]g(x)= 2x-1[/tex], [tex]h(x)= \sqrt{x}[/tex]

(fogoh)(9)= f(g(h(9))

To find f(g(h(9)), first we find h(9)

[tex]h(x)= \sqrt{x}[/tex]

[tex]h(9)= \sqrt{9}=3[/tex]

Now we replace 3 for h(9)

f(g(h(9))= f(g(3)

We find g(3) using g(x)

[tex]g(x)= 2x-1[/tex]

[tex]g(3)= 2(3)-1=5[/tex]

Replace g(3) by 5

f(g(h(9))= f(g(3)=f(5)

Now we find f(5) using f(x)

[tex]f(x)= 2x[/tex]

[tex]f(5)= 2(5)=10[/tex]

So (fogoh)(9)= 10