Question

Which of the following sets of ordered pairs represents a function?

{(5,2),(2,6),(5,10),(1,2)}
{(-3,2),(2,6),(5,2),(1,7)}
{(-3,2,(2,6),(3,10),(1,7)}
{(-3,2),(2,6),(5,10),(2,-1)}
^dont get this one..

Which expression is equal to
(f+g)(x)?

f(x)=x^2+3;g(x)=x-1

x^2+x+2
x^2+-2x+4 <__
x^3-x^2+3x-3
x^3-3<-

f(x)=2x+5;g(x)=3x^2

which expression is equal to
(Fog)(x)?

12x^2+60x+75
6x^2+5 <--
6x^2+56x^2+5
3x^2+2x+5

f(x)=4x-7;g(x)x+3
what is the value of (gof)(4)?

9
14
12
21<--

f(x)=10x-5
what is the value of f^-1(-4)
-35
0.1
0.01
-45 < yeah I really don't get this one neither.

Answer 1

Look up the definition of a function in your text or in your notes.
In a nutshell, it says that for every x there is one and only one y value
So, if you see two or more y values for the same x, then it is NOT a function
e.g. in the first I see (5,2) and (5,10) , so NOT a function
What do you notice about the others ?

#2
f(x)=x^2+3;g(x)=x-1
then (f+g)(x) =x^2 + 3 + x - 1
= x^2 + x + 2

#3 correct

#4
f(x)=4x-7;g(x)x+3
(gof)(4)
= g(f(4)) ---> f(4) = 16-7 = 9
= g(9) = 9+3 = 12


#5 f^-1 (x) means the inverse of the function

so if f(x) = 10x - 5
y = 10x - 5
inverse: interchange the x and y variables,
x = 10y - 5
now solve this for y
10y = x+5
y = (x+5)/10
f^-1 (x) = (x+5)/10
f^-1 (-4) = (-4+5)/10 = 1/10 = 0.1

notice when you compare y = 10x-5 and y = (x+5)/10
you are performing the inverse of each operation in reverse order
that is,
in the first: given any x you would first multiply it by 10 then subtract 5
for the inverse: given any x you would first add 5, then divide by 10
That is true for all inverses, and after doing a few you should be able to get the inverse without any steps.

Answer 2

Thank you again.