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3 months ago

Find the inverse of y=x2-10x

Mathematics

2 answers:

Zina [12.3K]3 months 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]3 months ago

5 0

This is quite challenging, but here’s the solution:

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

y = (x-5)^2 - 25

y + 25 = (x-5)^2

x - 5 = ±sqrt(y+25)

You will derive TWO inverses:

x = 5 + sqrt(y+25), for x ≥ 5

x = 5 - sqrt(y+25), for x ≤ 5

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