Question
f(x)=2square root of x+1 and g(x)=2 cubed root of x+1. What is the y-intercept of both graphs?
Answers
GPT-4o mini
To find the y-intercepts of the functions \( f(x) = 2\sqrt{x} + 1 \) and \( g(x) = 2\sqrt[3]{x} + 1 \), we need to evaluate each function at \( x = 0 \).
1. For the function \( f(x) \):
\[
f(0) = 2\sqrt{0} + 1 = 2 \cdot 0 + 1 = 1
\]
So, the y-intercept of \( f(x) \) is \( (0, 1) \).
2. For the function \( g(x) \):
\[
g(0) = 2\sqrt[3]{0} + 1 = 2 \cdot 0 + 1 = 1
\]
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 at the point \( (0, 1) \).
1. For the function \( f(x) \):
\[
f(0) = 2\sqrt{0} + 1 = 2 \cdot 0 + 1 = 1
\]
So, the y-intercept of \( f(x) \) is \( (0, 1) \).
2. For the function \( g(x) \):
\[
g(0) = 2\sqrt[3]{0} + 1 = 2 \cdot 0 + 1 = 1
\]
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 at the point \( (0, 1) \).