Question

given the two functions, which statement is true?
$f(x)=\sqrt{x + 1}+6$ and $g(x)=\sqrt3{x - 2}+6$
a the y - intercept of $f(x)$ and $g(x)$ are the same.
b the y - intercept of $f(x)$ is greater than the y - intercept of $g(x)$.
c neither function has a y - intercept.
d the y - intercept of $g(x)$ is greater than the y - intercept of $f(x)$.

Explanation:

Step1: Find y-intercept of $f(x)$

Substitute $x=0$ into $f(x)$:
$f(0)=\sqrt{0+1}+6 = \sqrt{1}+6 = 1+6=7$

Step2: Find y-intercept of $g(x)$

Substitute $x=0$ into $g(x)$:
$g(0)=\sqrt[3]{0-2}+6 = \sqrt[3]{-2}+6 \approx -1.26+6=4.74$

Step3: Compare the two intercepts

$7 > 4.74$, so the y-intercept of $f(x)$ is greater than that of $g(x)$.

Answer:

B. The y-intercept of $f(x)$ is greater than the y-intercept of $g(x)$.