Question

The function f(x) is shown below.

Answer 1

Answer:

Third option is correct.

Step-by-step explanation:

The given table is

 x       f(x)

–6      1

–3       2

 2       5

 5       3

 8       0

If the coordinates of a function f(x) is defined as (x,y), then the coordinates of inverse of f(x) is defined as (y,x).

$f(g(y))=f(x)$                  $[\because g(x)=(y,x)]$

$f(g(y))=y$                  $[\because f(x)=(x,y)]$

If g(x) is the inverse of f(x), then the value of f(g(y)) is y.

It is given that g(x) is the inverse of f(x), then the value of f(g(2)) is 2.

Therefore third option is correct.

Answer 2

Answer:

2

Step-by-step explanation:

x          f(x)

-6         1

-3         2

2           5

5           3

8           0

We will use two point slope form to find function

Formula :$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

$(x_1,y_1)=(-6,1) \\(x_2,y_2)= (-3,2)$

Substitute the values in the formula :

$y-1=\frac{2-1}{-3+6}(x+6)$

$y-1=\frac{1}{3}(x+6)$

$3y-3=x+6$

$3y=x+9$

$y=\frac{1}{3}x+3$

So, $f(x)=\frac{1}{3}x+3$

find the inverse of f(x)

$y=\frac{1}{3}x+3$

Substitute y =x and x = y

$x=\frac{1}{3}y+3$

$x-3=\frac{1}{3}y$

$3x-9=y$

So, $g(x)=3x-9$

Thus the inverse of f(x) = $g(x)=3x-9$

$f(g(x))=\frac{1}{3}(3x-9)+3$

Substitute x = 2

$f(g(2))=\frac{1}{3}(3(2)-9)+3$

$f(g(2))=2$

Hence the value of f(g(2)) is 2