Question

If f(x)=2x, g(x)= 2x-1, and h(x)= square root of x, find (fogoh)(9)

Answer 1

Answer:

10

Step-by-step explanation:

$f(x)= 2x$, $g(x)= 2x-1$, $h(x)= \sqrt{x}$

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

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

$h(x)= \sqrt{x}$

$h(9)= \sqrt{9}=3$

Now we replace 3 for h(9)

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

We find g(3) using g(x)

$g(x)= 2x-1$

$g(3)= 2(3)-1=5$

Replace g(3) by 5

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

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

$f(x)= 2x$

$f(5)= 2(5)=10$

So (fogoh)(9)= 10

Answer 2

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