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3 years ago

(6Q) Find the domain and range.

Mathematics

1 answer:

Rudik [331]3 years ago

8 0

Answer: Option a.

Domain: (-∞, ∞)

Range: (-∞, ∞)

Step-by-step explanation:

We have the function $f(x) = 2x + cosx$

Note that f(x) is the sum of two continuous functions $h(x) = 2x$ and $g(x) = cosx$

The domain and range of h(x) are all real numbers

The domain of g(x) is all real numbers. The range of g(x) is [-1, 1]

Then the domain of $f(x) = h(x) + g(x)$ will be the intersection of the domains of the function $h(x) = 2x$ and the function $g(x) = cosx$ .

Therefore the domain of f(x) are all real numbers. x ∈ (-∞, ∞)

The range of f(x) will be equal to the union of the range of g(x) and h(x)

Therefore the range will be all real numbers f(x) ∈ (-∞, ∞)

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3 years ago

In a bag of marbles 12% were blue 18% were green and the rest were purple if the bag has 150 marbles how many were blue or green

baherus [9]

Answer:

Step-by-step explanation:

12 % of the marbles are blue, and

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3 years ago

Triangle TUV was dilated to create triangle T'U'V' using point A as the center of dilation. What is the scale factor of the dila

Tomtit [17]

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In the dilation of triangle TUV, It is obvious that the image T'U'V' is smaller than the original triangle TUV and hence the scale factor is less than 1.

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3 years ago

Read 2 more answers

In a certain function, y varies directly with x. If y = 6 when x = 8, find x when y = 9.

Hatshy [7]

If y = 6 when x = 8, then value of "x" when y = 9 is equal to 12

Solution:

Given that , In a certain function, y varies directly with x

And x = 8 when y = 6,

We have to find what will be the value of x when y = 9

Now, from the given information,

$\begin{array}{l}{y \alpha x} \\\\ {y=c x \rightarrow(1)}\end{array}$

where c is the proportionality constant

$\begin{array}{l}{\text { Now, substitute } x=8 \text { and } y=6 \text { in }(1)} \\\\ {\rightarrow 8=c(6) \rightarrow c=\frac{8}{6}} \\\\ {\rightarrow c=\frac{4}{3}} \\\\ {\text { Then, }(1) \rightarrow x=\frac{4}{3} y} \\\\ {\text { So, when } y=9} \\\\ {\rightarrow x=\frac{4}{3}(9)} \\\\ {\rightarrow x=4 \times 3} \\\\ {\rightarrow x=12}\end{array}$