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.
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.
Thank you again.
To determine which sets of ordered pairs represent a function, we need to check if each x-value is paired with a unique y-value.
Let's analyze each set:
1. {(5,2),(2,6),(5,10),(1,2)}
In this set, the value of x=5 is paired with both y=2 and y=10. Therefore, this set does not represent a function.
2. {(-3,2),(2,6),(5,2),(1,7)}
Every x-value in this set is paired with a unique y-value. Therefore, this set represents a function.
3. {(-3,2),(2,6),(5,10),(2,-1)}
Here, the value of x=2 is paired with both y=6 and y=-1. Hence, this set does not represent a function.
Therefore, the second set, {(-3,2),(2,6),(5,2),(1,7)}, is the set that represents a function.
Moving on to the second question:
We are given two functions, f(x) = x^2 + 3 and g(x) = x - 1. We need to find (f+g)(x), which means we need to find the sum of f(x) and g(x).
(f+g)(x) = f(x) + g(x)
= (x^2 + 3) + (x - 1)
= x^2 + x + 2
Therefore, the expression that is equal to (f+g)(x) is x^2 + x + 2.
Next, let's determine the expression equal to (Fog)(x), where f(x) = 2x + 5 and g(x) = 3x^2:
(Fog)(x) = f(g(x))
= f(3x^2)
= 2(3x^2) + 5
= 6x^2 + 5
Hence, the expression equal to (Fog)(x) is 6x^2 + 5.
For the fourth question:
We are given f(x) = 4x - 7 and g(x) = x + 3. We need to find the value of (gof)(4), which means we need to compose the functions in the order g(f(x)) and evaluate it at x = 4.
gof(x) = g(f(x))
= g(4x - 7)
= (4x - 7) + 3
= 4x - 4
To find the value of (gof)(4), we substitute x = 4 in the expression:
(gof)(4) = 4(4) - 4
= 16 - 4
= 12
Therefore, the value of (gof)(4) is 12.
Lastly, for the fifth question:
We have f(x) = 10x - 5, and we need to find the value of f^-1(-4), which means we need to find the inverse of f(x) and evaluate it at x = -4.
To find the inverse of f(x), we need to switch the x and y variables and solve for y:
x = 10y - 5
10y = x + 5
y = (x + 5)/10
Therefore, the inverse of f(x) is f^-1(x) = (x + 5)/10.
To find the value of f^-1(-4), we substitute x = -4 in the expression:
f^-1(-4) = (-4 + 5)/10
= 1/10
= 0.1
Hence, the value of f^-1(-4) is 0.1.