F(x)=3x^2+8x+5 find value of f(a)

Mathematics

1 answer:

Korolek [52]3 years ago

7 0

f(a) = 3a² + 8a + 5

substitute x = a into f(x)

f(a) = 3a² + 8a + 5

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Refer to the image below. Red is increasing. Blue is decreasing.

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4. y is the angle between -π/2 and π/2, inclusive, whose sine equals x

5. QI and QII

6. QI and QIV

Step-by-step explanation:

4. Just as an exponent of -1 indicates the inverse (reciprocal) of a variable ...

$x^{-1}=\dfrac{1}{x}$

so an "exponent" of -1 on a function name indicates the inverse of the function. (The same notation is used to indicate the inverse of other things, as well.) That is, the notation ...

$y=\sin^{-1}{(x)}$

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Comment on the graph

The attached graph shows one full cycle of sine, cosine, and tangent functions. Each function has a portion highlighted by dots. The highlighted portion corresponds to the portion for which the inverse function is defined. This is a portion of the curve that passes the horizontal line test, so the result of the inverse function is single-valued as a function result must be.

I have also identified the angle quadrants as Q3, Q4, Q1, Q2. By comparing the dotted function sections to the quadrant identifiers, you can see the answers to problems 5 and 6.

The image of where the various inverse trig functions are defined is a good one to keep in your head whenever you're working with those functions.

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5. The arccos function is defined in quadrants I and II.

6. The arctan function is defined in quadrants IV and I.