SOLUTION: I need help evaluating this function. Given f(x)=1/[x], find f(2)+f(-2) and find f(c^2+4). I don't understand.

Algebra ->  Functions -> SOLUTION: I need help evaluating this function. Given f(x)=1/[x], find f(2)+f(-2) and find f(c^2+4). I don't understand.      Log On


   

Question 178998This question is from textbook
: I need help evaluating this function. Given f(x)=1/[x], find f(2)+f(-2) and find f(c^2+4). I don't understand. This question is from textbook

Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"Given f(x)=1/[x], find f(2)+f(-2)"

Is the function f%28x%29=1%2Fabs%28x%29? (ie is the right side 1 over the absolute value of "x")???


If so, then...


Let's find f(2)

f%28x%29=1%2Fabs%28x%29 Start with the given function


f%282%29=1%2Fabs%282%29 Plug in x=2


f%282%29=1%2F2 Take the absolute value of 2 to get 2


-------------------------------


Let's find f(-2)

f%28x%29=1%2Fabs%28x%29 Start with the given function


f%28-2%29=1%2Fabs%28-2%29 Plug in x=-2


f%28-2%29=1%2F2 Take the absolute value of -2 to get 2


Now let's add f(2) to f(-2):


f%282%29%2Bf%28-2%29=1%2F2%2B1%2F2=%281%2B1%29%2F2=2%2F2=1


So f%282%29%2Bf%28-2%29=1


----------------------------------------------------------

"Given f(x)=1/[x], find f(c^2+4)"


f%28x%29=1%2Fabs%28x%29 Start with the given function


f%28c%5E2%2B4%29=1%2Fabs%28c%5E2%2B4%29 Plug in x=c%5E2%2B4


From here, there's not much you can do to simplify.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

I'm presuming that your brackets around the x indicate absolute value.

We know that and

The other thing is, given f(x), to evaluate f(a), substitute a for x in the expression defining the function.

So if then





Therefore

Evaluate the same way.

You get

But!

Hence, for any real c

That means that for any real c.