Saturday

October 25, 2014

October 25, 2014

Posted by **Sébastien** on Sunday, May 13, 2012 at 10:41am.

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 -
**Bosnian**, Sunday, May 13, 2012 at 3:00pm1 )

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 -
**Sébastien**, Sunday, May 13, 2012 at 4:17pmThanks :)

**Answer this Question**

**Related Questions**

calcius - Determine whether the relation represents a function. If it is a ...

math - Consider the function f(x)= 3 ------. x^2-25 a) Determine any ...

college algebra - 1.for the given function f&g, find the following and state the...

math help please - Consider the function g(x)=x/x-7. a) Determine an equation ...

algebra - Find the domain and range of the relation and determine whether it is ...

math - determine the domain of the function y=log(subscript/little x)(8-x) so x^...

algebra - 1 (a) A function passes through the points (0, -5), (1, 0), (2, 7). ...

calc - How I can to determine the domain and the maximum and minimum local of ...

Math - What is the domain? Use a graphing utility to determine the intervals in ...

Math(Help!!) - What is the domain? Use a graphing utility to determine the ...