Which function has an inverse that is also a function?
1 answer:
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Answer:
Option D
Step-by-step explanation:
f(x) =
Transformed form of the function 'f' is 'g'.
g(x) =
Property of vertical stretch or compression of a function,
k(x) = x
Transformed function → m(x) = kx
Here, k = scale factor
1). If k > 1, function is vertically stretched.
2). If 0 < k < 1, function is vertically compressed.
From the given functions, k =
Since, k is between 0 and , function f(x) is vertically compressed by a scale factor
.
g(x) = f(x + 4) represents a shift of function 'f' by 4 units left.
g(x) = f(x - 4) represents a shift of function 'f' by 4 units right.
g(x) =
Therefore, function f(x) has been shifted by 4 units left to form image function g(x).
Option D is the answer.