Question

find the inverse of the function.
\\( y = (x + 5)^2 \\)
write your answer in the form \\( a pm bsqrt{cx + d} \\), where \\( a, b, c, \\) and \\( d \\) are constants. simplify any fractions.
\\( y = \\)

Explanation:

Step1: Swap x and y

To find the inverse of a function, we first swap the roles of \( x \) and \( y \). So starting with \( y=(x + 5)^2 \), we get \( x=(y + 5)^2 \).

Step2: Solve for y

Take the square root of both sides. Remember that when we take the square root, we have to consider both the positive and negative roots. So \( \pm\sqrt{x}=y + 5 \).

Step3: Isolate y

Subtract 5 from both sides to solve for \( y \). We get \( y=- 5\pm\sqrt{x} \). Comparing this with the form \( a\pm b\sqrt{cx + d} \), we have \( a=-5 \), \( b = 1 \), \( c=1 \), and \( d = 0 \).

Answer:

\( -5\pm\sqrt{x} \)