Question

consider the function $f(x) = 1 + \sqrt{x + 1}$. for which value of $x$ does $f(x) = 5$?
$x = \square$

Explanation:

Step1: Set up the equation

Set $f(x)=3$:
$$1+\sqrt{x+1}=3$$

Step2: Isolate the square root

Subtract 1 from both sides:
$$\sqrt{x+1}=3-1=2$$

Step3: Eliminate the square root

Square both sides:
$$x+1=2^2=4$$

Step4: Solve for x

Subtract 1 from both sides:
$$x=4-1=3$$

Answer:

$3$