Evaluate the function f\left(x\right)=5x+2\mid11-5x\mid-4f(x)=5x+2∣11−5x∣−4 for x = -5.

Mathematics

1 answer:

Anestetic [448]2 years ago

7 0

Answer:

$f\left(5\right) = 43$

Step-by-step explanation:

Given

$f\left(x\right)=5x+2\mid11-5x\mid-4$

Required

Solve for x = -5

This implies that we substitute -5 for x in $f\left(x\right)=5x+2\mid11-5x\mid-4$

$f\left(5\right)=5(-5)+2\mid11-5(-5)\mid-4$

Open all brackets

$f\left(5\right) = -25+2\mid11+25\mid-4$

$f\left(5\right) = -25+2\mid36\mid-4$

Absolute value of 36 is 36; Wo, we have:

$f\left(5\right) = -25+2*36-4$

$f\left(5\right) = -25+72-4$

$f\left(5\right) = 43$

You might be interested in

Show all work. <br><br>PLEASE HELP!!!!

34kurt

(a) Using the table, give the values fo rthe inverse

1) original table of values:

x      1     2     3    4    5

f(x)   0     1     1    5    3

2) The inverse of the function is obtained by exchanging x and f(x), this is:

                   ( x, f(x) ) → ( f(x), x)

3) So, the table of values of the inverse of the given function is:

x          0    1     1      5     3

f⁻¹ (x)   0     1     2     3     4

(b) Is the inverse a function?

No, the inverse is not a function, since the table of the inverse shows that the x -value 1 has two different images.

This ambigüity is opposite to the definition of a function, which requires that any input value has only one output. For that reason, the inverse is not a function. You cannot tell whether the image of 1 is 1 or 2, because both are images of the same value.

7 0

3 years ago

Now there is a door whose height is more than its width by 6 chi 8 cun. The distance between the [opposite] corners is 1 zhang.

Kaylis [27]

Answer:

height: 9 chi 6 cun
width: 2 chi 8 cun

Step-by-step explanation:

The factor-of-ten relationship between the different units means we can combine the numbers in decimal fashion. If 1 unit is 1 zhang, then 1 chi is 0.1 zhang and 1 cun is 0.01 zhang. Hence 6 chi 8 cun is 0.68 zhang.

Let x and y represent the width and height, respectively. In terms of zhang, we have ...

y - x = 0.68

x^2 +y^2 = 1^2

Substituting y = 0.68 +x into the second equation gives ...

x^2 + (x +0.68)^2 = 1

2x^2 +1.36x - 0.5376 = 0 . . . . . eliminate parentheses, subtract 1

Using the quadratic formula, we have ...

x = (-1.36 ±√(1.36^2 -4(2)(-0.5376)))/(2·2) = (-1.36 ±√6.1504)/4

x = 0.28 . . . . . the negative root is of no interest

y = 0.28 +0.68 = 0.96

In units of chi and cun, the dimensions are ...

height: 9 chi 6 cun