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Question

# state the domains and ranges of f and f^-1. f(x) = √x+1.

Solution

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The Domain of the function $f(x)=\sqrt{x+1}$ is the set of all real numbers greater than or equal to $-1$, $x\underline{>}-1$.

The Range of the function $f(x)=\sqrt{x+1}$ is the set of all real numbers greater than or equal to $0$, $y\underline{>}0$.

The Domain of the inverse function $f^{-1}(x)=x^2-1$ is the set of all real numbers greater than or equal to $0$, $x\underline{>}0$

The Range of the inverse function $f^{-1}(x)=x^2-1$ is the set of all real numbers greater than or equal to $-1$, $y\underline{>}-1$.

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