Solve for <em>x</em> when √(<em>x</em> ² - 4) = 1 :
√(<em>x</em> ² - 4) = 1
<em>x</em> ² - 4 = 1
<em>x</em> ² = 5
<em>x</em> = ±√5
We're looking at <em>x </em>≤ 0, so we take the negative square root, <em>x</em> = -√5.
This means <em>f</em> (-√5) = 1, or in terms of the inverse of <em>f</em>, we have <em>f</em> ⁻¹(1) = -√5.
Now apply the inverse function theorem:
If <em>f(a)</em> = <em>b</em>, then (<em>f</em> ⁻¹)'(<em>b</em>) = 1 / <em>f '(a)</em>.
We have
<em>f(x)</em> = √(<em>x</em> ² - 4) → <em>f '(x)</em> = <em>x</em> / √(<em>x</em> ² - 4)
So if <em>a</em> = -√5 and <em>b</em> = 1, we get
(<em>f</em> ⁻¹)'(1) = 1 / <em>f '</em> (-√5)
(<em>f</em> ⁻¹)'(1) = √((-√5)² - 4) / (-√5) = -1/√5
The sign must be negative; see the attached plot, and take note of the negatively-sloped tangent line to the inverse of <em>f</em> at <em>x</em> = 1.
That is false the opposite of 7 is -7
Answer:
(-3, 1)
Step-by-step explanation:
Answer:
3cm < Third side < 7cm
Thus third side can take any value between 3cm and 7 cm
(note: excluding 3 cm and 7 cm)
If the value are integral then possible values of third side are
4cm, 5cm,6cm
Step-by-step explanation:
This question can be solved using given by Triangle Inequality Theorem Given below.
- Sum of two sides is always greater than value of third side
- Difference of two sides is always less than value of third side
Given two sides are 2cm, 5cm
Sum of two sides = (2+5)cm = 7 cm
Difference of two sides = (5-2) = 3 cm
Let the third side be X
thus according to Triangle Inequality Theorem
X < Sum of two sides of given triangle
X < 7cm -----1
X > Difference of two sides
X > 3cm ----1
combining expression 1 and 2 we have
3cm < X < 7cm
Thus third side can take any value between 3cm and 7 cm
(note: excluding 3 cm and 7 cm)
If the value are integral then possible values are
4c, 5cm,6c
The answer would be C. Median.
