Which equation is the inverse of y 9x 2 4

Q: Which equation can be simplified to find the inverse of Y 5x2 10?

Summary: The inverse of the equation y = 5x2 + 10 is f-1(x) = y = √(x/5 - 2). x = 5y2 + 10 can be simplified to find the inverse.

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Algebra Examples
Gauthmathier0214
Gauthmathier0029
Which equation is the inverse of Y 9x 2 4 prime?
Which equation can be simplified to find the inverse of Y 5x2 10?

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July 19, 2021 at 7:10 pm #10289
Which equation is the inverse of y = 9x^2 – 4?
July 19, 2021 at 7:13 pm #10294
Answer: y = ± [ √(x+4) ] / 3
Solution:
1) To find the inverse of the function y = 9x2 – 4, exchange the variables x and y, and then solve for the new y.
2) Exchange of the variables: y = 9x2 – 4 → x = 9y2 – 4
3) Solve for y:
=> 9y2 = x + 4
=> y2 = [x + 4] / 9
=> y = ± [ √(x + 4) ] / 3
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Algebra Examples

Find the Inverse y=9x^2-4

Step 1

Interchange the variables.

Step 2

Rewrite the equation as .

Add to both sides of the equation.

Divide each term in by and simplify.

Cancel the common factor of .

Cancel the common factor.

Take the square root of both sides of the equation to eliminate the exponent on the left side.

Combine the numerators over the common denominator.

Factor the perfect power out of .

Pull terms out from under the radical.

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the to find the first solution.

Next, use the negative value of the to find the second solution.

The complete solution is the result of both the positive and negative portions of the solution.

Step 3

Replace with to show the final answer.

Step 4

Verify if is the inverse of .

The domain of the inverse is the range of the original function and vice versa. Find the domain and the range of and and compare them.

The range is the set of all valid values. Use the graph to find the range.

Interval Notation:

Set the radicand in greater than or equal to to find where the expression is defined.

Subtract from both sides of the inequality.

The domain is all values of that make the expression defined.

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Since the domain of is the range of and the range of is the domain of , then is the inverse of .

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Gauthmathier0214

Grade 12 · 2021-07-04

YES! We solved the question!

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Which equation is the inverse of Which equation is the inverse of y=9x2-4 ? - Gauthmath ?

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Gauthmathier0029

Grade 12 · 2021-07-04

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