Which one of the following is a possible expression for g(x)?
Consider the following for the next two (02) items that follow: Let f(x)=x^{2}-1 and g(f(x))=x-\sqrt{x}+1.
- A. \sqrt{x+1}-\sqrt{x+1}
- B. \sqrt{x+1}-\sqrt{x+1}+1 ✓
- C. \sqrt{x+1}+\sqrt{x+1}
- D. x+1-\sqrt{x+1}+1
Correct Answer: B. \sqrt{x+1}-\sqrt{x+1}+1
Explanation
We are given f(x) = x^2 - 1, which implies x^2 = f(x) + 1, so x = \sqrt{f(x)+1} for x \geq 0. We substitute x into the expression for g(f(x)): g(f(x)) = \sqrt{f(x)+1} - \sqrt{f(x)+1} + 1. Replacing f(x) with x gives the function g(x) = \sqrt{x+1} - \sqrt{x+1} + 1.
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