# Math

posted by .

hello I need help to do this exercise

Consider the function f (x) = (16 x + 33) / (x +3)
1) Determine its domain Df
2) Solve the equation f (x) = 14
3) Show that for all x in Df: f (x) - 15 = (x-12) / (x +3)
4) deduct the resolution of the inequality f (x)> 15.

Thanks for your help.

• Math -

1 )

The domain of a function is the set of all possible input values , which allows the function formula to work.

The denominator of any fraction cannot have the value zero.

I this case :

x + 3

must be different of zero

x different of - 3

Domain:

( - infinity , - 3 ) U ( - 3 , infinity )

OR

all values of x different of - 3

2 )

( 16 x + 33 ) / ( x + 3 ) = 14 Multiply both sides by ( x + 3 )

16 x + 33 = 14 * ( x + 3 )

16 x + 33 = 14 x + 14 * 3

16 x + 33 = 14 x + 42

16 x - 14 x = 42 - 33

2 x = 9 Divide both sides by 2

x = 9 / 2

3 )

f ( x ) - 15 =

( 16 x + 33 ) / ( x + 3 ) - 15 * ( x + 3 ) / ( x + 3 ) =

( 16 x + 33 - 15 x - 15 * 3 ) / ( x + 3 ) =

( x + 33 - 45 ) / ( x + 3 ) =

( x - 12 ) / ( x + 3 )

4 )

( 16 x + 33 ) / ( x + 3 ) > 15
Multiply both sides by ( x + 3 )

16 x + 33 > 15 * ( x + 3 )

16 x + 33 > 15 x + 15 * 3

16 x + 33 > 15 x + 45

16 x - 15 x > 45 - 33

x > 12

• Math -

Thanks :)

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More Similar Questions

Post a New Question
multiple_questions_with_answers

the text passage contains multiple mathematical questions along with their answers. the questions are:

1) determine the domain of the function f(x) = (16x + 33) / (x + 3)
2) solve the equation f(x) = 14
3) show that for all x in df: f(x) - 15 = (x - 12) / (x + 3)
4) solve the inequality f(x) > 15

answers are provided for each question in the text.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Math

posted by .

hello I need help to do this exercise

Consider the function f (x) = (16 x + 33) / (x +3)
1) Determine its domain Df
2) Solve the equation f (x) = 14
3) Show that for all x in Df: f (x) - 15 = (x-12) / (x +3)
4) deduct the resolution of the inequality f (x)> 15.

Thanks for your help.

• Math -

1 )

The domain of a function is the set of all possible input values , which allows the function formula to work.

The denominator of any fraction cannot have the value zero.

I this case :

x + 3

must be different of zero

x different of - 3

Domain:

( - infinity , - 3 ) U ( - 3 , infinity )

OR

all values of x different of - 3

2 )

( 16 x + 33 ) / ( x + 3 ) = 14 Multiply both sides by ( x + 3 )

16 x + 33 = 14 * ( x + 3 )

16 x + 33 = 14 x + 14 * 3

16 x + 33 = 14 x + 42

16 x - 14 x = 42 - 33

2 x = 9 Divide both sides by 2

x = 9 / 2

3 )

f ( x ) - 15 =

( 16 x + 33 ) / ( x + 3 ) - 15 * ( x + 3 ) / ( x + 3 ) =

( 16 x + 33 - 15 x - 15 * 3 ) / ( x + 3 ) =

( x + 33 - 45 ) / ( x + 3 ) =

( x - 12 ) / ( x + 3 )

4 )

( 16 x + 33 ) / ( x + 3 ) > 15
Multiply both sides by ( x + 3 )

16 x + 33 > 15 * ( x + 3 )

16 x + 33 > 15 x + 15 * 3

16 x + 33 > 15 x + 45

16 x - 15 x > 45 - 33

x > 12

• Math -

Thanks :)

## Similar Questions

1. ### algebra

1 (a) A function passes through the points (0, -5), (1, 0), (2, 7). Use finite differences to determine the equation of the function. (b) Draw the graph of the function. (c) Draw the inverse on the graph. (d) Show at least two different …
2. ### calcius

Determine whether the relation represents a function. If it is a function, state the domain and range. {(-2, 1), (-1, -2), (0, -3), (1, -2), (3, 6)} a. function domain: {-2, -1, 0, 1, 3} range: {1, -2, -3, 6} b. function domain: {1, …
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Consider the trig equation: 4sinxcos2x + 4cosxsin2x - 1 = 0 in the Interval [0, 2 pi] Either show that there is no solution to the equation in this domain, or determine the smallest possible solution.
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Find the inverse of the function f(x) = 5 – e^(x-1). Determine the domain, range, and asymptotes of the function and its inverse function. Please show all of your work.
5. ### MATH Graphing Domain

Consider the linear function with equation y = 3x + 5. Sketch the graph of the linear function on the grid. h t t p : //img402 . imageshack . us/img402/1466/picture38c . j p g Here is a picture of the graph, and this is how I did it. …
6. ### College Algebra

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7. ### pre-calculus

solve the equation 1. In x + In (x+12) =2 x= ?
8. ### math

Consider the function f(x)= 3 ------. x^2-25 a) Determine any restrictions on x. b) State the domain and range. c) State equation(s) for the asymptote(s). d) Determine any x- and y-intercepts. e) Sketch a graph of the function. f) …
9. ### math help please

Consider the function g(x)=x/x-7. a) Determine an equation for the vertical asymptote. b) State the domain. c) Determine an equation for the horizontal asymptote. d) State the range. e) Sketch the function. ( i will do it) f) Summarize …
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More Similar Questions

Post a New Question
user
TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS

The text passage contains multiple mathematical questions along with their answers. The questions are:

1) Determine the domain of the function f(x) = (16x + 33) / (x + 3)
2) Solve the equation f(x) = 14
3) Show that for all x in Df: f(x) - 15 = (x - 12) / (x + 3)
4) Solve the inequality f(x) > 15

Answers are provided for each question in the text.