Question

Suppose f(x) = (x + 1)² for x ≥ - 1. If g(x) is the function whose graph is the reflection of the graph of f(x) with respect to the line y = x, then g(x) equals

• A. $- \sqrt{x} - 1,$ x ≥ 0
• B. $\frac{1}{(x + 1)^{2}},x > - 1$
• C. $\sqrt{x + 1},$ x ≥ −1
• D. $\sqrt{x}$− 1, x ≥ 0

Answer 1

Answer: (D)

$\sqrt{x}$− 1, x ≥ 0

Answer 2

Given that f(x) = (x + 1)², x ≥ − 1

Now if g(x) is the reflection of f(x) in the line y = x than it can be obtained by interchanging x and y in f(x)

i.e., y = (x + 1)² change to x = (y + 1)²

⇒ y + 1 = $\sqrt{x}$

⇒ y = $\sqrt{x}$− 1 defined \overset{̶}{V}x ≥ 0

∴ g(x) = $\sqrt{x} - 1$, \overset{̶}{V} x ≥ 0.