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<- or b.
f(x)=2x+5;g(x)=3x^2
which expression is equal to
(Fog)(x)?
12x^2+60x+75
6x^2+5 <-- or D
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.
Which expression is equal to
(f+g)(x)?
f(x)=x^2+3;g(x)=x-1
(f+g)(x) is the same as f(x)+g(x). If f(x)=x^2+3 and g(x)=x-1, you can substitute them out. The expression becomes (x^2+3)+(x-1). Simplify
f(x)=2x+5;g(x)=3x^2
which expression is equal to
(Fog)(x)?
(Fog)(x) means f(x)*g(x). If f(x)=2x+5 and g(x)=3x^2, then you can substitute them. The expression becomes (2x+5)*(3x^2). Simplify
To determine which of the sets of ordered pairs represents a function, we need to check if there are any repeated x-values. If any x-value is repeated, then it is not a function.
Let's go through each set of ordered pairs:
1. {(5,2),(2,6),(5,10),(1,2)}:
In this set, the x-value 5 is repeated, so it is not a function.
2. {(-3,2),(2,6),(5,2),(1,7)}:
There are no repeated x-values in this set, so it is a function.
3. {(-3,2,(2,6),(3,10),(1,7)}:
There is a parenthesis error in this set, but assuming it is {(-3,2),(2,6),(3,10),(1,7)}, there are no repeated x-values, so it is a function.
4. {(-3,2),(2,6),(5,10),(2,-1)}:
The x-value 2 is repeated, so it is not a function.
Therefore, sets (2) {(-3,2),(2,6),(5,2),(1,7)} and (3) {(-3,2),(2,6),(3,10),(1,7)} represent functions.
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To find the expression that represents (f+g)(x), we need to add the expressions f(x) and g(x).
Given f(x) = x^2 + 3 and g(x) = x - 1, we can add them together:
(f+g)(x) = f(x) + g(x)
= (x^2 + 3) + (x - 1)
= x^2 + x + 2
Therefore, the expression (f+g)(x) is x^2 + x + 2.
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To find the expression that represents (Fog)(x), we need to substitute the expression for g(x) into f(x), wherever we see x.
Given f(x) = 2x + 5 and g(x) = 3x^2, we substitute g(x) into f(x):
(Fog)(x) = f(g(x))
= f(3x^2)
= 2(3x^2) + 5
= 6x^2 + 5
Therefore, the expression (Fog)(x) is 6x^2 + 5.
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To find the value of (gof)(4), we need to substitute the value x = 4 into the expression for g(x), and then use the result as the input for f(x).
Given f(x) = 4x - 7 and g(x) = x + 3:
Step 1: Find g(4):
g(4) = 4 + 3
= 7
Step 2: Substitute g(4) into f(x):
(gof)(4) = f(g(4))
= f(7)
= 4(7) - 7
= 28 - 7
= 21
Therefore, the value of (gof)(4) is 21.
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To find the value of f^(-1)(-4), we need to find the inverse of the function f(x) and then substitute -4 into the inverse function.
Given f(x) = 10x - 5:
Step 1: Replace f(x) with y: y = 10x - 5.
Step 2: Swap x and y: x = 10y - 5.
Step 3: Solve for y (inverse function):
x + 5 = 10y
y = (x + 5) / 10
Therefore, the inverse function of f(x) is f^(-1)(x) = (x + 5) / 10.
Step 4: Substitute -4 into f^(-1)(x):
f^(-1)(-4) = (-4 + 5) / 10
= 1 / 10
= 0.1
Therefore, the value of f^(-1)(-4) is 0.1.