What is the solution of the​ equation? Eliminate any extraneous solutions

Question

Let​ f(x)= x^2+6 and​ g(x) = x+8/x. Find ​(g◦​f)(-7)

Answer 1

Given:​ 

f(x)= x²+6

g(x) = x+8/x.

Therefore:

f(-7) = (-7)²+6 = 49+6=55

Find ​(g◦​f)(-7).

​(g◦​f)(-7) = g(f(-7))=g(55)

g(55) = 55+8/55 = 3025/55+8/55 = 3033/55

Check:

3033/55 = x+8/x

3033/55 = (x²+8)/x

(3033/55)x = x²+8

Multiply 55 both sides:

3033x = 55x²+440

0 = 55x² -3033x+440

0 = 55x² -3025x-8x+440

0 = 55x(x-55)-8(x-55)

0=(55x-8)(x-55)

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x-55 = 0 or 55x-8=0

x=55= f(-7)

Our answer is correct.