# How do you find the inverse of #f(x) = | x | - 3# and is it a function?

The inverse function of

We know that,

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

To find the inverse of the function ( f(x) = |x| - 3 ), follow these steps:

- Replace ( f(x) ) with ( y ).
- Swap the roles of ( x ) and ( y ).
- Solve for ( y ).
- Replace ( y ) with ( f^{-1}(x) ).

Doing this, we get:

[ x = |y| - 3 ]

Now, solve for ( y ):

[ x + 3 = |y| ]

Since the absolute value function can be rewritten as two separate equations, one for when ( y ) is positive and one for when ( y ) is negative, we have:

When ( y ) is positive:

[ y = x + 3 ]

When ( y ) is negative:

[ y = -x - 3 ]

Therefore, the inverse function, ( f^{-1}(x) ), consists of two separate equations:

[ f^{-1}(x) = \begin{cases} x + 3 & \text{if } x \geq 0 \ -x - 3 & \text{if } x < 0 \end{cases} ]

As for whether it is a function, yes, the inverse of ( f(x) = |x| - 3 ) is a function. Both equations in the inverse function pass the vertical line test, meaning each input value (or ( x ) value) corresponds to exactly one output value (or ( y ) value). Therefore, it is a function.

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

- How do you find the vertical, horizontal or slant asymptotes for #f(x) = (2x^2-5x-12)/(3x^2-11x-4 )#?
- How do you find the vertical, horizontal or slant asymptotes for # f(x) =sqrt(x^2+1)+2-x#?
- How do you determine if #4x^5 / absx # is an even or odd function?
- How do you find the domain and range of #y = log_2(x - 3)#?
- How do you find the horizontal and vertical asymptote of the following: #f(x) = (2x-3)/(x^2+2)#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7