Answer:
D
Step-by-step explanation:
Rotating 270 puts you in the 4th quadrant.
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.
Answer:
x = 5/3
Step-by-step explanation:
-3x+5
-5= -3x
-5/-3 = 5/3
Answer:
The area is 45 units squared
Step-by-step explanation:
If the rectangle's width is 3 units, and the length is 5 times then:
5 x 3 = 15
So the length is 15 units
The area is length times width
15 x 3 = 45
The area is 45 units squared
Answer: p=2
Step-by-step explanation: The first thing you should do is combine any like terms. For you this means combining 4p and -7p. This gives you -3p+5=-1. Then, subtract 5 on each side to eliminate the 5. This gives you -3p=-6. Divide by -3 on each side to allow the p to stand alone. This makes p=2.