Which function is the inverse of f(x) = (x − 3)^3 + 2?
2 answers:
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Answer:
Step-by-step explanation:
Required
The equation in slope intercept form
Solving (3):
The equation in slope intercept form is:
This gives:
Expand
Solving (5):
The equation in slope intercept form is:
This gives:
Expand
Given:
The two functions are:
To find:
The type of transformation from f(x) to g(x) in the problem above and including its distance moved.
Solution:
The transformation is defined as
.... (i)
Where, a is horizontal shift and b is vertical shift.
- If a>0, then the graph shifts a units left.
- If a<0, then the graph shifts a units right.
- If b>0, then the graph shifts b units up.
- If b<0, then the graph shifts b units down.
We have,
The function g(x) can be written as
...(ii)
On comparing (i) and (ii), we get
Therefore, the type of transformation is translation and the graph of f(x) shifts 2 units up to get the graph of g(x).