SOLUTION: Find a formula for the inverse of the function. f(x) = 6 − x2(x raised to the power of 2), x ≥ 0 f −1(x) = f(x) = 6 − x2, x ≥ 0 f −1(x) =

Algebra ->  Functions -> SOLUTION: Find a formula for the inverse of the function. f(x) = 6 − x2(x raised to the power of 2), x ≥ 0 f −1(x) = f(x) = 6 − x2, x ≥ 0 f −1(x) =       Log On


   

Question 1196463: Find a formula for the inverse of the function.
f(x) = 6 − x2(x raised to the power of 2), x ≥ 0
f −1(x) =

f(x) = 6 − x2, x ≥ 0
f −1(x) =


Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39618) About Me  (Show Source):
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Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

The standard template or outline to finding the inverse is this:
1) Replace f(x) with y
2) Swap x and y
3) Solve for y to find

So the steps look like this:
f%28x%29+=+6+-+x%5E2

y+=+6+-+x%5E2 Apply step 1

x+=+6+-+y%5E2 Apply step 2

x%2By%5E2+=+6

y%5E2+=+6-x

y+=+sqrt%286-x%29

The domain of f(x) is x+%3E=+0
The domain and range swap when going from the original function to the inverse (since the x and y swap roles)
This means the range of the inverse is y+%3E=+0 and it further means we'll focus on the positive version of the square root only. We won't have "plus/minus".

Answer: The inverse is