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3 years ago

Use the graph to determine which statement describes f(x)

Mathematics

1 answer:

djverab [1.8K]3 years ago

6 0

Answer:

f(x) does not have an inverse function, because its graph fails the horizontal line test. ⇒ A

Step-by-step explanation:

The vertical line test is used to show that the graph represents a

function or not

If the vertical line crosses the graph in more than one point, then the graph does not represent a function

If the vertical line crosses the graph in only one point in different positions, then the graph represents a function

The horizontal line test is used to show that the function has an

inverse or not

If the horizontal line crosses the graph of a function in more than one point, then the function has no inverse

If the horizontal line crosses the graph of a function in only one point in different positions, then the function has an inverse

Let us look at the given graph

→ The graph represents a parabola, which represents the function f(x)

∵ Any horizontal line drawn will cross the graph in more than one point

∴ f(x) has no inverse

∴ f(x) does not have an inverse function, because its graph fails the

horizontal line test.

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NEED HELP FAST!

mihalych1998 [28]

The answer is currently A so yep thats the answer ok

8 0

3 years ago

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Sofian's current age is (2x + 3) times Mastura's age. Given that Mastura's current age is (x + 5) years and 6 years ago, the sum

Sliva [168]

${\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}$

★ Sofian's current age is (2x + 3) times Mastura's age.

★ Mastura's current age is (x + 5) years

★ 6 years ago, the sum of their ages is 44 years.

${\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}$

★ The value of x.

${\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}$

According to the question,

Present age of Mastura = (x + 5) years

Present age of Sofian = (2x + 3) (x + 5) years, i.e :

$\longrightarrow \tt (2x + 3) (x + 5)$

$\longrightarrow \tt 2 {x}^{2} + 10x + 3x + 15$

$\longrightarrow \tt 2 {x}^{2} + 13x + 15 \: years$

Now,

Mastura's age 6 years ago = (x + 5) - 6

=> x + 5 - 6

=> x - 1

Sofian's age 6 years ago = 2x² + 13x + 15 - 6

= 2x² + 13x + 9

Using the condition provided by the question, 

Mastura's age 6 years ago + Sofian's age 6 years ago = 44

$\longrightarrow \tt (x - 1) + (2 {x}^{2} + 13x + 9) = 44$

$\longrightarrow \tt x - 1 + 2 {x}^{2} + 13x + 9 = 44$

$\longrightarrow \tt 2 {x}^{2} + 14x + 8 = 44$

$\longrightarrow \tt 2 {x}^{2} + 14x + 8 - 44 = 0$

$\longrightarrow \tt 2 {x}^{2} + 14x - 36= 0$

• Taking "2" common.

$\longrightarrow \tt 2 ({x}^{2} + 7x - 18) = 0$

$\longrightarrow \tt {x}^{2} + 7x - 18 = \dfrac{0}{2}$

$\longrightarrow \tt {x}^{2} + 7x - 18= 0$

• Using splitting the middle term

$\longrightarrow \tt {x}^{2} + 9x - 2x - 18 = 0$

$\longrightarrow \tt x(x + 9) - 2(x + 9) = 0$

$\longrightarrow \tt (x + 9) (x - 2) = 0$

either $\tt (x + 9) = 0 \: \: or \: \: (x - 2) = 0$

$\longrightarrow \tt x = - 9 \: \: or \: \: x = 2$

[As the age cannot be negative. So x = - 9 is rejected]

$\therefore \tt \: x = \red{ 2}$

${\large{\textsf{\textbf{\underline{\underline{Verification :}}}}}}$

According to the condition provided by the question, 

• Mastura's age 6 years ago + Sofian's age 6 years ago = 44

$\longrightarrow \tt x - 1 + 2 {x}^{2} + 13x + 9 = 44$

Putting x = 2 we get,

$\longrightarrow \tt 2 - 1 + 2( {2})^{2} + 13(2) + 9 = 44$

$\longrightarrow \tt 1 + 2 \times 4 + 26+ 9 = 44$

$\longrightarrow \tt 1 + 8 + 26+ 9 = 44$

$\longrightarrow \tt 9 + 26+ 9 = 44$

$\longrightarrow \tt 18 + 26 = 44$

$\longrightarrow \tt 44 = 44$

Hence verified.

$\begin{gathered} {\underline{\rule{290pt}{3pt}}} \end{gathered}$

Hope it helps you! :))

6 0

3 years ago

What is the value of x in the solution to the system of equations? 4x - 2y = 5 y = 3x - 1

saw5 [17]

Answer:

X = 7

Step-by-step explanation:

Please mark brainliest.

4 0

4 years ago

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The length is 3 inches more than the width period the width is 2 inches more than the height. The volume is 120 in.³. What is th

Debora [2.8K]

Answer:

the dimension of the box is : 8 by 5 by 3

Length = 8

Width = 5

Height = 3

Step-by-step explanation:

Let x,y and z represent the length, width and height of the box.

Given;

The length is 3 inches more than the width

x = y+3 .......1

the width is 2 inches more than the height

y = z + 2

z = y-2 .........2

Volume = length×width×height = xyz = 120 in^3

xyz = 120 ........3

Substituting equation 1 and 2 into 3

(y+3)×y ×(y-2) = 120

y(y^2+y-6) = 120

y^3 + y^2 - 6y - 120 = 0

Solving the polynomial equation we have;

y = 5

From equation 1;

x = y+3 = 5+3

x = 8

From equation 2;

z = y-2 = 5-2

z = 3

Therefore, the dimension of the box is

8 by 5 by 3

Length = 8

Width = 5

Height = 3

4 0

3 years ago

Math question plssss help

Alecsey [184]

Answer:

Step-by-step explanation:

8 0

3 years ago

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