Answer:
Domain of f(x): All real values.
Range of f(x): All real values.
Domain of f -1(x): All real values.
Range of f -1(x): All real values
Step-by-step explanation:
We are given the following function:
Since it is a line, we have that both the domain is the range is the real set.
Inverse function:
The domain of the inverse function is the range of the original function, and the range of the inverse function is the domain of the original function.
Finding the inverse function:
Exchange x and y in the original function, and isolate y. So
Original
Exchanging:
Isolating y:
Answer:
no no
Step-by-step explanation:
nah nahnah nahnah nahnah nahnah nahnah nahnah nah
Answer: a) y = f(x - 6)
b) y = f(x) - 2
<u>Step-by-step explanation:</u>
For transformations we use the following formula: y = a f(x - h) + k
- a = vertical stretch
- h = horizontal shift (positive = right, negative = left)
- k = vertical stretch (positive = up, negative = down)
a) f(x) has a vertex at (-1, 1)
M has a vertex at (5, 1)
The vertex shifted 6 units to the right → h = +6
Input h = +6 into the equation and disregard "a" and "k" since those didn't change. ⇒ y = f(x - 6)
b) f(x) has a vertex at (-1, 1)
N has a vertex at (-1, -1)
The vertex shifted down 2 units → k = -2
Input k = -2 into the equation and disregard "a" and "h" since those didn't change. ⇒ y = f(x) - 2
