can someone help and check over the work

Question

 Let f(x) = (x - 9)/(x + 2)

(a) Calculate f(-3). I got f=-4 for this. or if i didn't finish the entire equation it would be -3f=12

would i finish the equation for this?

 

f(-3)=(-3)-9/(-3)+2

-3f=-12/(-3)+2

-3f=-12/-1

-3f=12

 

-3f/-3=12/-3

f=-4

 

(b) State the domain of the function f(x) = (x - 9)/(x + 2)

?

(c) Find f(a-1)

 

I am not really sure on this one. what I did was...

 

f(a-1)=x-9/x+2

f(a-1)=(a-1)-9/(a-1)+2

 

Not really sure how i would solve this. would i time the (a-1) by the -9 and +2? or would i just make it -10a and 1a? any help in the right direction would be grand.


 

Answer 1

Hi Lindsay.

 

a) For f(-3) you just substitute -3 for x in the function.

f(-3) = [(-3)-9]/[(-3)+2]

f(-3) = -12/-1

f(-3) = -12

Regarding your solution, your first line is correct.  Your error is in multiplying the function by -3 in your second line.

 

b) The domain of a function is the set of values of x which make the function solvable.

To do this, look at the denominator and set it equal to 0

In this case

x+2=0

Solve for x

x=-2

If x=-2, we would have a 0 in the denominator and remember we can't divide by 0.

So the domain would be

(-∞,-2)u(-2,∞)  Notice I have used (next to the -2 indicating the -2 is not included in the solution

Another way to write this is

{x=R:x≠-2}

 

c)  Your initial setup is correct.  Substitute (a-1) for x

f(a-1) = [(a-1) - 9]/[(a-1) + 2]

Let's get rid of the parenthesis on the right side so perhaps this will be a bit clearer

f(a-1) = [a-1 - 9]/[a-1 + 2]

which is equivalent to

f(a-1) = [a-10]/[a+1]

This is the solution.  Notice that the constants in this function are the original constants -1 since the value of x is a-1.

 

Hope this helps.