# Math

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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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