Math
posted by Sébastien on .
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 = (x12) / (x +3)
4) deduct the resolution of the inequality f (x)> 15.
Thanks for your help.

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 
Thanks :)