Compare the graphs of f(x)=2x+1−−−−−√ and g(x)=2^3√x+1−−−−− . What is the y-intercept of both graphs?

Answer 1

To compare the graphs of the functions $f(x)=\sqrt{2x+1}$ and $g(x)=\sqrt[3]{2x+1}$, we can start with finding their y-intercepts.

The y-intercept of a function is found by evaluating the function at $x=0$.

1. Finding the y-intercept of $f(x)$: $$f(0)=\sqrt{2(0)+1}=\sqrt{1}=1$$ So, the y-intercept of $f(x)$ is $(0,1)$.

2. Finding the y-intercept of $g(x)$: $$g(0)=\sqrt[3]{2(0)+1}=\sqrt[3]{1}=1$$ So, the y-intercept of $g(x)$ is also $(0,1)$.

In conclusion, both functions $f(x)$ and $g(x)$ have the same y-intercept, which is $(0,1)$.