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bulgar [2K]
3 years ago
11

Evaluate the following without using the calculator

Mathematics
1 answer:
s2008m [1.1K]3 years ago
5 0

\sec x=\dfrac{1}{\cos x}\to \sec60^o=\dfrac{1}{\cos60^o}\\\\\text{Use the table of values of a trigonometric functions}\\\\\cos30^o=\dfrac{\sqrt3}{2}\\\\\sin\dfrac{\pi}{4}=\dfrac{\sqrt2}{2}\\\\\cos60^o=\dfrac{1}{2}\to\sec60^o=\dfrac{1}{\frac{1}{2}}=2\\\\\text{Substitute:}\\\\\cos30^o\sin\dfrac{\pi}{4}+\dfrac{\sec60^o}{3}=\dfrac{\sqrt3}{2}\cdot\dfrac{\sqrt2}{2}+\dfrac{2}{3}=\dfrac{\sqrt6}{4}+\dfrac{2}{3}\\\\=\dfrac{3\sqrt6}{3\cdot4}+\dfrac{4\cdot2}{4\cdot3}=\dfrac{3\sqrt6}{12}+\dfrac{8}{12}\\\\=\boxed{\dfrac{8+3\sqrt6}{12}}

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Which is the correct answer?<br><br>(explain how you got your answer)​
Otrada [13]

Answer:

Option B. f¯¹(x) = ³√(– x – 9)

Step-by-step explanation:

From the question given above:

f(x) = – x³ – 9

f¯¹(x) =?

We can obtain the inverse f¯¹(x) of the above equation by doing the following:

f(x) = – x³ – 9

Replace f(x) with y

y = – x³ – 9

Interchange x and y

x = – y³ – 9

Make y the subject . This is illustrated below:

x = – y³ – 9

Rearrange

x + 9 = – y³

Multiply through by –1

–(x + 9) = y³

y³ = – x – 9

Take the cube root of both side

y = ³√(– x – 9)

Replace y with f¯¹(x)

f¯¹(x) = ³√(– x – 9)

Thus, the inverse of the function

f(x) = – x³ – 9

is

f¯¹(x) = ³√(– x – 9)

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