If f(x)=x^2-1 what is the equation for f^-1(x)
1 answer:
Answer:
see below
Step-by-step explanation:
Swap y and x, then solve for y.
Original:
... y = f(x) = x² -1
Swap y and x:
... x = y² -1
Add 1:
... x + 1 = y²
Take the square root:
... ±√(x+1) = y . . . . . matches the 3rd selection
Rewrite as the inverse relation: (not a function)
... f^-1(x) = ±√(x+1)
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<em>Comment on the graph</em>
The attached graph shows the function f(x) in red, and the inverse relation g(x) in blue. You will note that g(x) is double-valued for most values of x, so is not a function. The function and its inverse relation are mirror images of each other in the line y=x. (That is, swapping y and x changes the function to its inverse, and vice versa.)
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Answer:
(a) AH < HC is No
(b) AH < AC is Yes
(c) △AHC ≅ △AHB is Yes
Step-by-step explanation:
Given
See attachment for triangle
Solving (a): AH < HC
Line AH divides the triangle into two equal right-angled triangles which are: ABH and ACH (both right-angled at H).
To get the lengths of AH and HC, we need to first determine the measure of angles HAC and ACH. The largest of those angles will determine the longest of AH and HC. Since the measure of the angles are unknown, then we can not say for sure that AH < HC because the possible relationship between both lines are: AH < HC, AH = HC and AH > HC
Hence: AH < HC is No
Solving (b): AH < AC
Length AC represents the hypotenuse of triangle ACH, hence it is the longest length of ACH.
This means that:
AH < AC is Yes
Solving (c): △AHC ≅ △AHB
This has been addresed in (a);
Hence:
△AHC ≅ △AHB is Yes
