The table below shows some inputs and outputs of the invertible function with domain all real numbers.

Mathematics

1 answer:

gizmo_the_mogwai [7]3 years ago

6 0

Answer:

f⁻¹(-2) = 3 and f⁻¹(1) = 0.

Step-by-step explanation:

By the definition of inverse functions:

$\displaystyle \text{If } f(a) = b\text{, then } f^{-1}(b) = a$

From the table, note that f(3) = -2.

Then by definition, f⁻¹(-2) = 3.

Likewise, f(0) = 1.

Then by definition, f⁻¹(1) = 0.

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In a free-fall experiment, an object is dropped from a height of h = 400 feet. A camera on the ground 500 ft from the point of i

PilotLPTM [1.2K]

Hmmm the object, is at rest, when dropped, so it has a velocity of 0 ft/s

the only force acting on the object, is gravity, using feet will then be -32ft/s²,

was wondering myself on -32 or 32.. but anyhow... we'll settle for the negative value, since it seems to be just a bit of convention issues

so, we'll do the integral to get v(t) then

$\bf \displaystyle \int -32\cdot dt\implies -32t+C
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\textit{object moves from \underline{rest}, so velocity is 0 at 0secs}
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-32(0)+C=0\implies C=0\implies \boxed{v(t)=-32t}
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\textit{now to get the positional s(t)}
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\displaystyle \int -32t\cdot dt\implies -16t^2+C
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\textit{the initial \underline{position} was 400ft away at 0secs}
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-16(0)^2+C=400\implies C=400\implies \boxed{s(t)=-16t^2+400}$

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part B) check the picture below