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3 years ago

Find the inverse of the function. y = x2 + 4x + 4

2 answers:

7 0

The given function is ⇒⇒⇒ y = x² + 4x + 4

To find the inverse of the function, we need to make x as a function of y and at the final step make a switch between x and y (i.e. make x as y and y as x)
y = x² + 4x + 4 ⇒⇒⇒ factor the quadratic equation
y = (x+2)(x+2)
y = (x+2)² ⇒⇒⇒ take the square root to both sides
√y = x+2
x = √y - 2 ⇒⇒⇒ x becomes a function of y
final step:
∴ y = √x - 2 ⇒⇒⇒ the inverse of the given function

So, as a conclusion:
f(x) = y = x² + 4x + 4 ⇒⇒⇒ the given function

f⁻¹(x) = y = √x - 2 ⇒⇒⇒ the inverse of the given function

Sever21 [200]3 years ago

3 0

The answer is the third one

y=+-√x-2

Hopes this helps, and God bless <3

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