Find f-1(x) if f(x) = 2x/3-4

Given:

The function is:

[tex]f(x)=\dfrac{2x}{3}-4[/tex]

To find:

The inverse of the given function, i.e., [tex]f^{-1}(x)[/tex].

Solution:

We have,

[tex]f(x)=\dfrac{2x}{3}-4[/tex]

Step 1: Substitute [tex]f(x)=y[/tex].

[tex]y=\dfrac{2x}{3}-4[/tex]

Step 2: Interchange x and y.

[tex]x=\dfrac{2y}{3}-4[/tex]

Step 3: Isolate y.

[tex]x+4=\dfrac{2y}{3}[/tex]

[tex]3(x+4)=2y[/tex]

[tex]\dfrac{3x+12}{2}=y[/tex]

[tex]\dfrac{3}{2}x+6=y[/tex]

Step 4: Substitute [tex]y=f^{-1}(x)[/tex].

[tex]f^{-1}(x)=\dfrac{3}{2}x+6[/tex]

Therefore, the inverse of the given function is [tex]f^{-1}(x)=\dfrac{3}{2}x+6[/tex].

what is the volume of the prism below?

Simon wants to earn as many points as possible in one turn in a game. Two number cubes whose sides are numbered 1 through 6 are rolled. He is given two options for the manner in which points are awarded in the turn.

OPTION A: If the sum of the rolls is a prime number, Simon receives 15 points.
OPTION B: If the sum of the rolls is a multiple of 3, Simon receives 12 points.

Which statement best explains the option he should choose?


A. Simon should choose Option B. The mathematical expectation of this option is 6.25 and is the greater mathematical expectation of the two options.

B. Simon should choose Option A. The mathematical expectation of this option is 6.25 and is the greater mathematical expectation of the two options.

C. Simon should choose Option B. The mathematical expectation of this option is 4 and is the greater mathematical expectation of the two options.

D. Simon should choose Option A. The mathematical expectation of this option is 4 and is the greater mathematical expectation of the two options.

At a restaurant your family spends $45.00 on lunch. If they want to leave a 15%
tip, How much should they leave as a tip for the waitress?
$67.50
$6.75
$4.50

If the exterior angles measurements of a hexagon are: 28°, 45°, 63°, 57º and 81°, find
the measure of the sixth exterior angle.

The area of a rectangle is 20 mm2. If the width is 4 mm, find the length?

I-ready question 6 which is the graph of y=3/4x-3

PLEASE HELP ME NOW ASAP I HAVE A MIN LEFT

Will give brainliest! Please help

Two numbers have a sum of - 6 and a product of 9.
Use the quadratic equation n^2 - 6n + 9 = 0 to determine the two numbers.
n2 - 6n + 9 = 0

(2a²b 5)2 (ab 332
22(a²b-c-3)(a?c%)

PLSSSSSSSSS HELPP WILL GIVE BRAINLIEST PLSSS

Help me out here please.

I need help please! DON'T USE LINKS! WILL BE REPORTED

This is 7th grade math

Evaluate the expression.use scientific notation to express your answer 4.8x10-8/3x10-3

Four out of 25 people are left-handed. In a school of 400 people, how many would you expect to be
left-handed

please answer asap need answer

The image of point (-1, 7) under a reflection across the y-axis is (-1, -7). *
True
False

Select ALL the correct answers.
Carmen and Matt are conducting different chemistry experiments in school. In both experiments, each student starts with an initial amount of water in a flask. They combine two chemicals which react to produce more water. Carmen's experiment starts with 30 milliliters of water in a flask, and the water increases in volume by 8.5 milliliters per second. Matt's experiment starts with 10 milliliters of water and increases in volume by 28% each second.




Which two conclusions can be made if f represents the volume of water in Carmen's flask and g represents the volume of water in Matt's flask?

The volume of water in Carmen's flask is increasing at a faster rate than the volume of water in Matt's flask over the interval [6, 8].
The volume of water in Carmen's flask is increasing at a slower rate than the volume of water in Matt's flask over the interval [4, 6].
The volume of water in Carmen's flask will always be greater than the volume of water in Matt's flask.
The volume of water in Matt's flask will eventually be greater than the volume of water in Carmen's flask.
The volume of water in Carmen's flask is increasing at a slower rate than the volume of water in Matt's flask over the interval [0, 2].

PLEASE HELP - Basketballs used in NBA games all have a diameter of approximately 912 in. inches. About how many cubic inches of air is contained in the spherical ball?

What is the correct ordering on a number line from left to right of these four numbers: - 2/3, 5/8, -3/5, -1/2

When three squares are joined at their vertices to form a right triangle, the combined area of the two smaller squares is the same as the area of the largest square. Which three squares will support this statement?

PLEASE HELP!


Please answer each question by the order ! So do 1. Etc.. 2. Etc.. to keep it organized! Thank u !:))

Simply the following expression: 12x + 5x - 8x

Which of the following student below will qualify for a grant?

If x^2 − 4x + 4 = 49, then what is x

Scott stood on a 42 in. high chair, then jumped into a 8 in.
deep hole. Which equation applies to his action?

Help ASAP I’ll mark you as brainlister

If three bakers can prepare 15
cakes in 60 minutes, if they
continue working at the same
rate, how many cakes can they
make in 3 hours?

I need an answer! NO LINKS PLS! il give brainlist