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Helga [31]
2 years ago
7

Algebraically determine the inverse of the function f(x)= 12x2+5.

Mathematics
1 answer:
aivan3 [116]2 years ago
7 0

Answer:

Step-by-step explanation:

f(x)= 12x2+5 should be written as  f(x) = 12x^2 + 5; the " ^ " symbol signifies exponentiation and is mandatory.

Here's how we find the inverse function.

1.  Apply the horizontal line test.  if a horizontal line intersects the graph in more than one place, the function is not one-to-one and does not have an inverse for all x.  However, if we focus on only [0, infinity), this part of the graph does have an inverse, which we can find as follows:

2.  Replace 'f(x)' with 'y:  y = 12x^2 + 5

3.  Interchange x and y:  x = 12y^2 + 5

                                                              x - 5

4.  Solve for y:  12y^2 = x - 5;   y^2 = ------------

                                                                12

                          x - 5

               y = √(----------)

                             12

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Jobisdone [24]

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The quickest way to get rid of a fraction is to multiply both

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So in this problem, we can get rid of the fraction in our

first step by multiplying both sides of the equation by 4.

On the left, the 4's cancel and on the right, 1(4) is 4.

Now we have h - 13 = 4.

Since 13 is being subtracted from <em>h</em>, to get <em>h</em> by itself,

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Now, we can check our answer by plugging 17 back

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3 years ago
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Natali [406]
The answer to what the length of the leg would be is 15.

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So our equation could be that a or b leg equals 20, it doesn’t matter which one.

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20^2 is 400 and 25^2 is 625.

Our equation now comes to 400 + b^2 = 625.

Now we take 400 and subtract it from
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So 625 - 400 comes out to be 225.

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