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Suppose `f(x)=(x+1)^2forxgeq-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)`equal.`a-sqrt(x)-1,xgeq0`(b) `1/((x+1)^2),x >-1``sqrt(x+1,)xgeq-1`(d) `sqrt(x)-1,xgeq0`A. `1-sqrt(x)-1, x ge 0`B. `(1)/((x+1)^(2)),x gt -1 `C. `sqrt(x+1), x ge -1`D. `sqrt(x)-1, x ge 0` |
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Answer» Correct Answer - D Given that `f(x)=(x+1)^(2), x ge -1.` Now, if g(x) is the reflection of f(x) in the line y = x, then g(x) is an inverse function of `y = f(x).` Given `y=(x+1)^(2) (x ge -1 and y ge 0)` ` or x = +- sqrt(y)-1` ` or g(x) =f^(-1)(x)=sqrt(x)-1, x ge 0` |
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