Verified Answer :

pegah

for these kinds of questions you should first solve for x:
y +36 = x^2 ⇒ √y+36 = x 
now the inverse of this equation is:
√x + 36 = y :)))
i hope this is helpful
have a nice day

Answer:

\(y=\sqrt{x+36}\)

Step-by-step explanation:

Since, for finding the inverse of a function f(x) we follow the following steps,

Step 1 : Replace f(x) by y,

Step 2 : Interchange x and y,

Step 3 : isolate y in the left side,

Step 4 : Replace y by \(f^{-1}(x)\)

Given equation is,

\(y=x^2-36\)

Here, we do not need to apply step 1 and step 4,

Now, Interchange x and y,

\(x=y^2-36\)

\(-y^2=-x-36\)

\(y^2=x+36\)

Taking square root both sides,

\(y=\sqrt{x+36}\)

Which is the required equation of inverse of the given equation.

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