Question

Which points lie on the graph of f(x) = log9x?

-1/81, 2
0,1
1/9, -1
3, 243
9,1
81,2

Answer 1

Let

y=f(x)

so
y=log9x

we know that

applying property of logarithms

y= log9x is equal to

$9^{y}=x$ ------> 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

$9^{2}=81$

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

$9^{1}=9$

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

$9^{-1}=1/9$

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

$9^{243}$

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

$9^{1}= 9$

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

$9^{2}=81$

81 is equal to 81-------> the point belongs to the graph

Answer 2

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;

• 1/9, -1

• 81, 2

Reasons:

The given function is f(x) = log₉x

Therefore;

$9^{f(x)} = x$

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 = $\frac{1}{9}$, f(x) = -1 ;

9⁻¹ = $\frac{1}{9}$, which corresponds with the form $9^{f(x)} = x$, therefore

• ( $\frac{1}{9}$, -1) is a point that lies in the graph of f(x) = log₉x

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 $9^{f(x)} = x$, and therefore, lie on the graph of the function.

• ( 81, 2) lies in the graph of f(x) = log₉x

Learn more here:

https://brainly.com/question/18845182