Mathematics, 15.07.2019 16:30 gpere9282

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

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Answer from: dajeourcrazy15

Let

y=f(x)

so
y=log9x

we know that

applying property of logarithms

y= log9x is equal to

$9^{y}=x$ ------> equation 1

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 from: jeremiaht7

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, -181, 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

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Answer from: Quest

5104.38 inches

step-by-step explanation:

Answer from: Quest

The point (5, 10) will work for the rule y=x+5.y= 10 x= 510=5+510=10therefore the ordered pair (5, 10) works for the rule

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