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3 years ago

49 POINTS!!!!!!!! PLZ HELP!

Mathematics

1 answer:

monitta3 years ago

7 0

Answer:

(a) f⁻¹(x) = 2x - 8

(b) f⁻¹(4) = 0

Step-by-step explanation:

This is usually not too difficult if you write the equation as y = f(x), then swap x and y and solve for y.

... y = (1/2)x + 4 . . . . y = f(x)

... x = (1/2)y + 4 . . . . variables swapped

... x - 4 = (1/2)y . . . . . subtract 4

... 2(x -4) = y . . . . . . multiply by 2

... y = 2x - 8 . . . . . . simplify

... f⁻¹(x) = 2x -8

____

Evaluating this for x=4, we get

... f⁻¹(4) = 2·4 - 8 = 0

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stealth61 [152]

$\large\underline{\sf{Solution-}}$

We have to evaluate the given expression.

$\rm = \sqrt{ \dfrac{1 - \sin(x) }{1 + \sin(x) } }$

If we multiple both numerator and denominator by 1 - sin(x), then the value remains same. Let's do that.

$\rm = \sqrt{ \dfrac{[1 - \sin(x)][1 - \sin(x) ]}{[1 + \sin(x)][1 - \sin(x) ]} }$

$\rm = \sqrt{ \dfrac{[1 - \sin(x)]^{2}}{1- \sin^{2} (x) } }$

We know that:

$\rm \longmapsto { \sin}^{2}(x) + \cos^{2}(x) = 1$

$\rm \longmapsto \cos^{2}(x) = 1 - { \sin}^{2}(x)$

Therefore, the expression becomes:

$\rm = \sqrt{ \dfrac{[1 - \sin(x)]^{2}}{\cos^{2} (x)}}$

$\rm = \dfrac{1 - \sin(x)}{\cos(x)}$

$\rm = \dfrac{1}{\cos(x)} - \dfrac{ \sin(x) }{ \cos(x) }$

$\rm = \sec(x) - \tan(x)$

7 0

3 years ago

Read 2 more answers

Plz help with this (PLZ NO LINKS!!!!)

Anna007 [38]

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7 0

3 years ago

Read 2 more answers

In slope-intercept form, write the equation of the line passing through the points (-4,1) and (-3,2).

Marina86 [1]

Answer:

the points are starting at 5y and the slope line goes up to (6, 1) and goes down to (-1, 4 ), (-2, 3), (-3, 2) and (-4, 1) The graph has 1x +5

going to desmos to graph it out you can see the slpe line going through (-4, 1) (-3, 2)

4 0

3 years ago

Is 8/6 equivalent to 16/12 as a ratio

valentina_108 [34]

Answer:

they are equivalent

Step-by-step explanation:

8/6

Divide the top and bottom by 2

4/3

16/12

Divide the top and bottom by 4

4/3

They are the same so they are equivalent

6 0

3 years ago

Read 2 more answers

How to compare 10.5 to 11 and 19

Marizza181 [45]

Answer:

Line up the decimal points. **Answer is Least to greatest: 10.5 , 11, 19**

Step-by-step explanation:

You need to line each number up.

10.5

11.0

19.0

The reason why 11 and 19 have a decimal point and zero at the end is because you need to do that in order to compare the numbers.

This problem is also a little common sense because 10.5 is the smallest, 19 is the largest while 11 is in the middle.

4 0

2 years ago