The function f(x) is shown below.

x
f(x)
–6
1
–3
2
2
5
5
3
8
0

if g(x) is the inverse of f(x), what is the value of f(g(
–6
–3
2
5

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).

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.

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 :

Substitute the values in the formula :

So,

find the inverse of f(x)

Substitute y =x and x = y

So,

Thus the inverse of f(x) =

Substitute x = 2

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

none.

step-by-step explanation:

m

1

=

5

m1=5

b

=

−

1

b=-1

find the slope and y-intercept of the second equation.

tap for more

m

2

=

0

m2=0

b

=

−

6

b=-6

compare the slopes

m

m of the two equations.

m

1

=

5

,

m

2

=

0

m1=5,m2=0

compare the two slopes in the decimal form. if the slopes are equal, then the lines are parallel. if the slopes are not equal, then the lines are not parallel.

m

1

=

5

,

m

2

=

0

m1=5,m2=0