Question

the table gives values of $f(x)$ and $g(x)$ for all positive integers, $x \leq 5$. given that $f(g(a))=g(g(4))$ where $a$ is a positive integer less than or equal to 5, what is the value of $a$?

$x$

$f(x)$

$g(x)$

---

---

---

1

3

2

2

4

5

3

2

4

4

5

1

5

1

3

select one answera 1b 2c 3d 5

Explanation:

Step1: Find $g(4)$ from table

Look up $x=4$ in $g(x)$ column: $g(4)=1$

Step2: Calculate $g(g(4))$

Substitute $g(4)=1$, find $g(1)=2$, so $g(g(4))=2$

Step3: Set $f(g(a))=2$, find $g(a)$

Look for $f(x)=2$ in table: $x=3$, so $g(a)=3$

Step4: Find $a$ for $g(a)=3$

Look up $g(x)=3$ in table: $x=5$, so $a=5$

Answer:

D. 5