How do you find the inverse of #y= -x# and is it a function?

Answer 1

See below.

For the inverse of a function we have to express #x# as a function of #y#:

#y=-x#

Multiply by #=1#

#x=-y#

Substitute:

#x=y#

#f^-1(x)=-x#

The function is its own inverse.

Since the inverse of a function is the reflection of the function in the line #y=x#, and #y=-x# is perpendicular to #y=x#, it is its own inverse.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To find the inverse of (y = -x), follow these steps:

  1. Replace (y) with (x) and (x) with (y).
  2. Solve the resulting equation for (y).
  3. The solution obtained represents the inverse function.

Starting with (y = -x):

  1. Swap (x) and (y): (x = -y)
  2. Solve for (y): (y = -x)

Therefore, the inverse of (y = -x) is (y = -x).

Yes, (y = -x) is a function because each input value (x-coordinate) corresponds to exactly one output value (y-coordinate), satisfying the definition of a function.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7