Let f(x) = x2 − 81. Find f−1(x).

1 answer:

3 0

F(x) = x² - 81

Finding f⁻¹(x) the inverse function

Let y = f(x) and solve for x.

y = x² - 81

y + 81 = x²

x² = y + 81

x = √(y + 81)

Recall f(x) = y, that means x = f⁻¹(y)

x = √(y + 81)

f⁻¹(y) = √(y + 81)

Therefore f⁻¹(x) = √(x + 81)

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Solve the system of equations using substitution y=x-1 and y=-2x+5

pav-90 [236]

Since the two equations equal y, set them equal to each other.

x-1=-2x+5

From there, solve for x.

First get x on one side, by using the addition property of equality.

x-1=-2x+5
3x-1=5

Isolate x by adding 1.
3x=6

Lastly get x all by itself by dividing each side by 3.
x=2

You can now substitute your x-value, 2, into one of the equations (or both, if you wish; either one will result in the same answer.)

y=x-1
y=2-1
y=1

OR

y=-2x+5
y=-2(2)+5
y=-4+5
y=1

Final answer:
x=2 and y=1

Any questions or anything you would like me to clarify, feel free to ask :)

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3 years ago

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Answer:

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Step-by-step explanation:

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2 years ago