FunctionHard
Question
Suppose, f(x) = (x + 1)2 for x ≥ - 1 If g (x) is the function whose graph is reflection of the graph of f (x) with respect to the line y = x, then g (x) equals
Options
A.- √x - 1, x ≥ 0
B.
, x > - 1
, x > - 1C.
, x ≥ - 1
, x ≥ - 1D.√x - 1, x≥ 0
Solution
It is only to find the inverse.
Let y = f(x) = (x + 1)2 for x ≥ -1
= x + 1, x ≥ - 1
⇒ √y = x + 1 ⇒ y ≥ 0, x + 1 ≥
⇒ x = √y - 1
⇒ f -1(y) = √y - 1
⇒ f -1(x) = √x - 1, x ≥ 0
Let y = f(x) = (x + 1)2 for x ≥ -1
= x + 1, x ≥ - 1⇒ √y = x + 1 ⇒ y ≥ 0, x + 1 ≥
⇒ x = √y - 1
⇒ f -1(y) = √y - 1
⇒ f -1(x) = √x - 1, x ≥ 0
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