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1 month ago

14

Find the inverse of y=x2-10x

2 answers:

Zina [12.3K]1 month ago

7 0

Answer:

$y=5\pm \sqrt{(25+x)}$

Step-by-step explanation:

We need to determine the inverse of the function $y=x^2-10x$ .

To find the inverse, we need to swap the x and y values and then solve for y.

After this interchange, we can express it as:

$x=y^2-10y$

Rearranging gives us:

$y^2-10y=x$

$y^2-10y-x=x-x$

$y^2-10y-x=0$

Utilizing the quadratic formula, we solve for y:

$y=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$y=\frac{-(-10)\pm \sqrt{(-10)^2-4(1)(-x)}}{2(1)}$

$y=\frac{10\pm \sqrt{100+4x}}{2}$

$y=\frac{10\pm \sqrt{4*25+4x}}{2}$

$y=\frac{10\pm \sqrt{4(25+x)}}{2}$

$y=\frac{10\pm 2\sqrt{(25+x)}}{2}$

$y=5\pm \sqrt{(25+x)}$

Hence, the inverse function for the original function is $y=5\pm \sqrt{(25+x)}$ .

AnnZ [12.3K]1 month ago

5 0

<span>This is quite challenging, but here’s the solution:
</span>

y = x^2 - 10x + 25 - 25

<span> y = (x-5)^2 - 25</span>

<span> y + 25 = (x-5)^2</span>

<span> x - 5 = ±sqrt(y+25)</span>

<span> You will derive TWO inverses:</span>

<span> x = 5 + sqrt(y+25),</span> for x ≥ 5

<span> x = 5 - sqrt(y+25),</span> for x ≤ 5

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