Question

f(x)=2square root x+1 and g(x)=2 cubed root x+1. What is the y-intercept of both graphs?

Answer 1

To find the y-intercepts of the functions \( f(x) \) and \( g(x) \), we need to evaluate each function at \( x = 0 \).

1. **Finding the y-intercept of \( f(x) \)**:

\[
f(x) = 2\sqrt{x} + 1
\]

Substitute \( x = 0 \):

\[
f(0) = 2\sqrt{0} + 1 = 2 \cdot 0 + 1 = 1
\]

So, the y-intercept of \( f(x) \) is \( (0, 1) \).

2. **Finding the y-intercept of \( g(x) \)**:

\[
g(x) = 2\sqrt[3]{x} + 1
\]

Substitute \( x = 0 \):

\[
g(0) = 2\sqrt[3]{0} + 1 = 2 \cdot 0 + 1 = 1
\]

So, the y-intercept of \( g(x) \) is also \( (0, 1) \).

### Conclusion:

- The y-intercept of \( f(x) \) is \( (0, 1) \).
- The y-intercept of \( g(x) \) is \( (0, 1) \).

Both functions have the same y-intercept.