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1 year ago

Given the function f(x) = 3x, find the value of f−1(81).

1 answer:

4 0

Given the function f (x) = 3x, find the value of f-1 (81).
For this case, the first thing you should do is rewrite the function.
We have then:
y = 3 ^ x
From here, we clear the value of x:
log3 (y) = log3 (3 ^ x)
log3 (y) = x
Then, we rewrite the function again:
f (x) ^ - 1 = log3 (x)
Now, we evaluate the inverse function for x = 81:
f (81) ^ - 1 = log3 (81)
f (x) ^ - 1 = 4
Answer:
the value of f-1 (81) is:
f (x) ^ - 1 = 4

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Venita is factoring the expression 32 a b minus 8 b. She determines the GCF and writes the factored expression as 8 b (4 a minus

never [62]

Answer:

She subtracted the GCF from the second term in the expression instead of dividing.

Step-by-step explanation:

Given the expression 32ab-8b, to find the common greatest factor, we will bring out a function that us common to both terms 32ab and 8b. To do that, we need to first find their individual factors as shown:

32ab = (2×2×2)×2×2×a×(b)

8b = (2×2×2×b)

From both factors, the common terms are the values in parenthesis i.e 2×2×2×b = 8b

Hence the GCF of the expression 32ab - 8b is 8b. On factoring out 8b from the expression we will have;

= 32ab - 8b

= 8b(32ab/8b - 8b/8b)

= 8b(4a-1)

Comparing the gotten equation with Venita's own, 8b(4a-0), we can say that she correctly factored out the GCF but her error was that she subtracted 8b from the second term of the expression instead of dividing by 8b. 8b-8b is what gives her 0 making her expression wrong. She should have divided her second term also by 8b to have 8b/8b which results in 1 instead of 0 that venita got.

7 0

1 year ago

Read 2 more answers

Which products result in a difference of squares? Select three options. A. (x minus y)(y minus x) B. (6 minus y)(6 minus y) C. (

solniwko [45]

Answer:

Step-by-step explanation:

Hello, please consider the following.

A. (x minus y)(y minus x)

$(x-y)(y-x)=-(x-y)(x-y)=-(x-y)^2$

This is not a difference of squares.

B. (6 minus y)(6 minus y)

$(6-y)(6-y)=(6-y)^2$

This is not a difference of squares.

C. (3 + x z)(negative 3 + x z)

This is a difference of squares.

$\boxed{(3+xz)(-3+xz)=(xz+3)(xz-3)=(xz)^2-3^2}$

D. (y squared minus x y)(y squared + x y)

This is a difference of squares.

$\boxed{(y^2-xy)(y^2+xy)=(y^2)^2-(xy)^2}$

E. (64 y squared + x squared)(negative x squared + 64 y squared)

This is a difference of squares.

$\boxed{(64y^2+x^2)(-x^2+64y^2)=(64y^2+x^2)(64y^2-x^2)=(64y^2)^2-(x^2)^2}$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

6 0

1 year ago

Read 2 more answers

Jackson buys a grape snow cone on a hot day. By the time he eats all the "snow" off the top, the paper cone is filled with 27\pi

anyanavicka [17]

Question:

Jackson buys a grape snow cone on a hot day. By the time he eats all the "snow" off the top, the paper cone is filled with 27\pi27π27, pi cm^3 3 start superscript, 3, end superscript of melted purple liquid. The radius of the cone is 333 cm. What is the height of the cone?

Answer:

The height of the cone is $9 \ cm$

Explanation:

It is given that the radius of the cone is $3 \ cm$

The volume of the cone is $27\pi$

The height of the cone can be determine using the formula,

$V=\frac{1}{3} \pi r^{2} h$

Substituting the values $V=27 \pi$ and $r=3$ , we get,

$27 \pi=\frac{1}{3} \pi(3)^{2} h$

Multiplying both sides by 3, we have,

$81 \pi= 9\pi h$

Dividing both sides by $9 \pi$ , we have,

$9=h$

Thus, the height of the cone is $9 \ cm$

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2 years ago

Which equation has only one solution?

notka56 [123]

Absolute value cannot be less than 0
Solve Absolute Value.|x−5|=−1No solutions.

|−6−2x|=8
x=−7 or x=1

|5x+10|=10
x=0 or x=−4

|−6x+3|=0
 $x = \frac{1}{2}$

So your answer is D) |–6x + 3| = 0

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1 year ago

450x2y5 3,000x4y3 What is the least common multiple (LCM) of these monomials?

ivolga24 [154]

The LCM would be 14.. your textbook would be really helpful

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2 years ago