Answer:
This is a many-to-one function as the value of y = -1 corresponds to two values of x:
Step-by-step explanation:
<u>Function</u>
A special relationship where each input (x-value) has a single output (y-value).
A function is <u>one-to-one</u> if each value in the range (y-values) corresponds to exactly one value in the domain (x-values).
A function is <u>many-to-one</u> if some values in the range (y-values) correspond to more than one (many) value in the domain (x-values).
This is a many-to-one function as the value of y = -1 corresponds to two values of x:
This is not a function as the value of x = -5 corresponds to two values of y:
This is not a function as the value of x = -2 corresponds to two values of y:
This is not a function as the value of x = -4 corresponds to two values of y:
Answer:
The answer is C
Step-by-step explanation:
I took this quiz before
Remark
The reason you are not getting many replies to this is an uncertainty about f(x). We do not know if you mean f(x) = 2/(x - 6) or f(x) = (2/x) - 6. We'll try it both ways.
First Way f(x) = 2/(x - 6)
f(x = y = 2/(x - 6) Interchange x and y
x = 2 / (y - 6) Multiply both sides by y - 6
x(y - 6) = 2 Divide by x
y - 6 = 2/x Add 6 to both sides.
y = 2/x + 6 Which is close to g(x) but it is not the same thing, even if you use x as a common denominator. That would give you
Second Way: f(x) = (2/x) - 6
f(x) = y = (2/x) - 6 Interchange x and y
x = (2/y) - 6 Add 6 to both sides
x + 6 = 2/y Multiply both sides by y
y(x + 6) = 2 Divide by sides by (x + 6)
y = 2/(x + 6)
Comment
These do not look anything alike so g(x) and f(x) are not inverses.