Question

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

Answer 1

`\bf \begin{cases} f(x)=2x\\ g(x)=2x-1\\ h(x)=√(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√(x)-1 \\\\\\ f[\ g(\ h(x)\ )\ ]=2[\ g(\ h(x)\ )\ ]\implies 2(2√(x)-1) \\\\\\ f[\ g(\ h(\quad 9\quad )\ )\ ]=2(2√(9)-1)\implies 4√(9)-1\implies 4\cdot 3-1\implies 11`

Answer 2

10

Explanation:

`f(x)= 2x`,
`g(x)= 2x-1`,
`h(x)= √(x)`

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

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

`h(x)= √(x)`

`h(9)= √(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