Question

2.7 Q9
The functions f and g are defined by the following tables. Use the tables to evaluate the given composite function.

Answer 1

Answer: $(gof)(-1)=-2$

Step-by-step explanation:

By definition, a composite function is a function formed by substituing one function into another function.

Given the composite function:

$(gof)(-1)$

You can rewrite it in the following form:

$g(f(-1))$

In order to evaluate it, follow these steps:

- Based on the table of the function f(x), the ouput value for $x=-1$ is $y=3$. Then:

$f(-1)=3$

- This will be the input of the function g(x).

- Notice in the table of the function g(x) that the output value when $x=3$ is $y=-2$:

$g(3)=-2$

Therefore:

$g(f(-1))=-2$ or $(gof)(-1)=-2$

Answer 2

Answer:

The value of $\rm{gof(-1)}$ is -2.

Step-by-step explanation:

Given,

The table contains the functional value of f(x) and g(x).

To find:   $\rm{gof(-1)}$

$\rm{fog(-1)}$ is a composite function of f(x) and g(x).

$\rm{gof(-1)}=\rm{g[f(-1)}]$

Clearly from the table, the value of f(x) when $x=-1$ is 3.

Therefore,

$f(-1)=3$

Now,

$\rm{gof(-1)}=\rm{g[f(-1)}]\\\rm{fof(-1)}=\rm{g(3)}$

Clearly from the table, the value of g(x) when $x=3$ is -2.

Thus,

$\rm{gof(-1)}=-2$

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