Answer:
Let
y=f(x)
so
y=log9x
we know that
applying property of logarithms
y= log9x is equal to
------> equation 1
so
case 1) (-1/81, 2)
x=-1/81
y=2
substitute the value of y in the equation 1 to obtain the value of x
81 is not equal to -1/81-------> the point does not belong to the graph
case 2) (0, 1)
x=0
y=1
substitute the value of y in the equation 1 to obtain the value of x
9 is not equal to 0-------> the point does not belong to the graph
case 3) (1/9, -1)
x=1/9
y=-1
substitute the value of y in the equation 1 to obtain the value of x
1/9 is equal to 1/9-------> the point belongs to the graph
case 4) (3, 243)
x=3
y=243
substitute the value of y in the equation 1 to obtain the value of x
9^{243} is not equal to 3-------> the point does not belong to the graph
case 5) (9, 1)
x=9
y=1
substitute the value of y in the equation 1 to obtain the value of x
9 is equal to 9-------> the point belongs to the graph
case 6) (81, 2)
x=81
y=2
substitute the value of y in the equation 1 to obtain the value of x
81 is equal to 81-------> the point belongs to the graph