Evaluate Composite Functions

Example on evaluating composite functions .

Example 1


$f(x)$ and $g(x)$ are functions defined by the tables of values below. What is the value of $f(g(-5))$?

$x$ $f(x)$
$-10$ $0$
$0$ $3$
$2$ $6$
$3$ $7$
$6$ $21$
$x$ $g(x)$
$-10$ $-20$
$-8$ $-10$
$-5$ $0$
$-4$ $3$
$-3$ $5$



  1. $0$
  2. $-10$
  3. $3$
  4. $7$
  5. $-5$

Solution


  1. We first use the table to determine g(-5)
    $g(-5)=0$

  2. We next substitute $g(-5)$ by $0$ in $f(g(-5))$

    $f(g(-5))=f(0)$
  3. We now use the table to determine $f(0)$.

    $f(g(-5))=f(0)=3$

    Answer C