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2 years ago

Which is the inverse of the function f (x) = 1/4x + 1/2

Mathematics

1 answer:

kiruha [24]2 years ago

7 0

Answer:

f⁻¹(x) = 4x - 2

Step-by-step explanation:

To find the inverse of a function, switch the places of x and y (or f(x)).

f(x) = 1/4x + 1/2 → y = 1/4x + 1/2

Switch the variables.

x = 1/4y + 1/2

Now you want to convert the equation back into y = mx + b form.

x = 1/4y + 1/2

Subtract 1/2 from both sides.

x - 1/2 = 1/4y

Now, you want to isolate y further by dividing both sides by 1/4 (or multiplying by 4).

4(x - 1/2) = y

Distribute the 4.

4x - 2 = y → y = 4x - 2 → f⁻¹(x) = 4x - 2

This is the inverse of your given function.

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How many solutions does the system have? y=−2x+4

Anna11 [10]

Answer:

There is only one solution and the solution is (0,4).

Step-by-step explanation:

The given system has equations;

$y=-2x+4$

and

$y=x^2-2x+4$

We equate the two equations to determine their point of intersection;

$x^2-2x+4=-2x+4$

$\Rightarrow x^2-2x+2x+4-4=0$

$\Rightarrow x^2=0$

$\Rightarrow x=0$

We put x=0 into the first equation to get;

$y=-2(0)+4=4$

There is only one solution and the solution is (0,4).

3 0

2 years ago

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sineoko [7]

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7 0

2 years ago

Find the slope and the y-intercept of the graph of the linear equation. 1. y=3x-7 2. y-1=-2/3x

ELEN [110]

Answer:

1) Slope: 3; y-intercept: -7

2) Slope: 2/3; y-intercept: 1

Step-by-step explanation:

y = mx + b; m is slope and b is y-intercept

1. y = 3x - 7

The equation is already in slope-intercept form, so you can find the slope and intercept.

Slope: 3

y-intercept: -7

2. y - 1 = 2/3x

For this one, you have to convert this into slope-intercept form (solving for y)

y - 1 = 2/3x

Add 1 to both sides

y - 1 + 1 = 2/3x + 1

y = 2/3x + 1

Now that the equation is in slope-intercept form, you can get the slope and y-intercept.

Slope: 2/3

y-intercept: 1

5 0

2 years ago

Solve the following equation:<br> 30= |- 4y + 2|

photoshop1234 [79]

Suppose $-4y+2\ge0$ . Then by definition of absolute value,

$|-4y+2| = -4y+2 \implies 30 = -4y+2 \implies -4y = 28 \implies \boxed{y=-7}$

On the other hand, suppose $-4y+2$ . Then

$|-4y+2| = -(-4y+2) \implies 30 = 4y - 2 \implies 4y = 32 \implies \boxed{y=8}$

Recall the definition,

$|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}$

3 0

1 year ago

Which statement about the pair of equations is true?

denpristay [2]

I say the answer I c. sorry if I'm wrong tho

7 0

3 years ago