Which points lie on the graph of f(x) = log9x? -1/81, 2 0,1 1/9, -1 3, 243 9,1 81,2

Let

y=f(x)

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

The function is such that, performing the reverse operations of the function

on the output gives the input.

The points that lie on the graph are;

Reasons:

The given function is f(x) = log₉x

Therefore;

The ordered pair are in the form (x, f(x))

First option gives;

9² =  81 ≠ -1/81, therefore, (-1/81, 2) does not lie on the graph of f(x)

Second option;

9¹ = 9 ≠ 0, the second option is not on a point on the graph

Third option, x = , f(x) = -1 ;

9⁻¹ = , which corresponds with the form , therefore

Fourth option:

9¹ = 9 ≠ 1, does not lie on the graph

Fifth option, x = 81, y = 2;

9² = 81, therefore, the fifth option ordered pair can be obtained or expressed in the form , and therefore, lie on the graph of the function.

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