Question

1. Write the inverse of equation of the function f(x) = x^2 - 4? 2. Sketch the inverse of the function f(x)= x^2 - 4 on graphing paper. Remember that the inverse graph should look identical in shape to the original, only flipped or rotated in some way. You equation should represent the equation you provided in #1. 3. You should notice that your graph in #2 is not a function. Choose part of the graph that would represent a function when graphed on its own. Highlight this portion of your graph . 4. Now that you have a function highlighted in #3, what are the domain and range of this highlighted function? (We are asking you to find the restricted domain and range of the inverse equation from #1 that makes this an inverse function on its own).

Answer 1

Answer: 1)
`\pm √(x+4)`

2) see graph

3) Choose one color from the graph

4) D: x ≥ -4

R: y ≥ 0 for
`√(x+4)` or y ≤ 0 for
`-√(x+4)`

Explanation:

1) To find the inverse, swap the x's and y's and solve for y:

Given: y = x² - 4

Swap: x = y² - 4

x + 4 = y²

`\pm √(x+4)=y`

2) see attachment. Red and Blue combined creates the graph of the inverse.

3) Choose either the positive (red graph) or the negative (blue graph).

red graph:
`y= √(x+4)`

blue graph:
`y= -√(x+4)`

4) Domain reflects the x-values of the function. The x-values for the red graph is the same as the blue graph so the answer will be the same regardless of which equation you choose.

Domain: x ≥ 0

Range reflects the y-values of the function. The y-values differ between the positive and negative inverse functions. Positive is above the x-axis. Negative is below the x-axis.

Range (red graph): y ≥ 0 for
`y= √(x+4)`

Range (blue graph): y ≤ 0 for
`y= -√(x+4)`