Compare the graphs of f(x) = sqrt(x) + 1 and g(x) = sqrt(x+1). Which one of the fol...
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Problem
Compare the graphs of f(x) = sqrt(x) + 1 and g(x) = sqrt(x+1). Which one of the following options is true?
Step-by-step solution
Both functions $f(x) = \sqrt{x} + 1$ and $g(x) = \sqrt{x+1}$ are increasing functions on their respective domains. The domain of $f(x)$ is $x \ge 0$ and the domain of $g(x)$ is $x \ge -1$. Both functions have a range of $y \ge 1$.
Answer
Both functions are increasing on their domain.