f(x) help show work

Question

Let f(x)=(2x-3)/(x+5)

(a)Calculate f(-2)

(b) State the domain of the function f(x)=2x-3/x+5

(c) Find and simplify as much as possible: f(t+1) . Show work.

Answer 1

Hi Theresa,

 

Firstly, keep in mind that f(x) denotes a function.  It does NOT mean, f times x.

Ok, for part a, substitute -2 anywhere you see an x like so, f(-2) = (2(-2) - 3)/((-2)+5).

Then simplify.  Your turn! f(-2) = ?

 

For part b, you must state all the valid values of x.  To do this, think about x cannot be.  What number would cause us to divide by zero which is not allowed.  The domain is all real numbers except this number.  What is it?

 

For part c, similar to part a, plug in t+1 anywhere you see an x.  We have, f(t+1) = (2(t+1) - 3)/((t+1) +5).  Next, simplify.  I'll leave this up to you.

 

Notice how I used parenthesis.  Very important.