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kaheart [24]
3 years ago
8

F(x)=

alt=" \frac{4x - 7}{10} " align="absmiddle" class="latex-formula">
then what is f^-1(x)​
Mathematics
1 answer:
Naily [24]3 years ago
7 0

Answer:

To find f-¹(x) of f(x) equate f(x) to y

That's

f(x) = y

So we have

y =  \frac{4x - 7}{10}

Next interchange the variables that's x becomes y and y becomes x

That's

x =  \frac{4y - 7}{10}

Next make y the subject

Cross multiply

We have

4y - 7 = 10x

Move -7 to the right side of the equation

4y = 10x + 7

Divide both sides by 4

We have the final answer as

y =  \frac{10x + 7}{4}

So

f ^{ - 1} (x) =  \frac{10x + 7}{4}

Hope this helps you

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Which statement is true about the extreme value of the given quadratic equation? y = -3x2 + 12x − 33
Zina [86]

Answer:

The equation has a maximum value with a y-coordinate of -21.

Step-by-step explanation:

Given

y =-3x^2 + 12x - 33

Required

The true statement about the extreme value

First, write out the leading coefficient

Leading = -3

-3 < 0 means that the function would be a downward parabola;

Downward parabola always have their vertex on top of the parabola and as such, the function has a maximum value.

The maximum value is:

x = -\frac{b}{2a}

Where:

a= -3; b =12; c =-33

So, we have:

x = -\frac{12}{2 * -3}

x = -\frac{12}{-6}

x =2

Substitute x =2 in y =-3x^2 + 12x - 33

y = -3*2^2 + 12 * 2 - 33

y = -21

<em>Hence, the maximum is -21.</em>

8 0
3 years ago
Which is the graph of f(x) = StartRoot x EndRoot?
shusha [124]

Answer:

The 4th graph

Step-by-step explanation:

To determine which graph corresponds to the f(x) = \sqrt{x}   we will start with inserting some values for x and see what y values we will obtain and then compare it with graphs.

f(1) = \sqrt{1} = 1\\f(2) = \sqrt{2} \approx 1.41\\f(4) = \sqrt{4} = 2\\f(9) = \sqrt{9} = 3

So, we can see that the pairs (1, 1), (2, 1.41), (4, 2), (3, 9) correspond to the fourth graph.

Do not be confused with the third graph - you can see that on the third graph there are also negative y values, which cannot be the case with the f(x) =\sqrt{x}, the range of that function is [0, \infty>,   so there are only positive y values for f(x) = \sqrt{x}

6 0
3 years ago
F(x)=3x-4 and g(x) = x2 find the value of f(3)-g(2) <br><br> show all work
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Answer: 1

f(x) = 3x - 4 => f(3) = 3.3 - 4 = 9 - 4 = 5

g(x) = x² => g(2) = 2² = 4

=> f(3) - g(2) = 5 - 4 = 1

Step-by-step explanation:

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