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Choose the inverse of y = x2 – 10x.

Choose the inverse of y = x2 – 10x.-example-1

2 Answers

9 votes

Answer:


y=\pm√(x+25)+5

Explanation:

Given function:


y=x^2-10x

Rearrange to make
x the subject.

First, complete the square by adding 25 to both sides and factoring:


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


y+25=(x-5)^2

Square root both sides:


\pm√(y+25)=x-5

Add 5 to both sides:


x=\pm√(y+25)+5

Finally, swap
x and
y (since the inverse of a function is its reflection in the line
y = x)


y=\pm√(x+25)+5

User Madoka
by
8.1k points
6 votes

Answer:

The inverse is 5±sqrt(x+25)

Explanation:

y = x^2 - 10x

To find the inverse, exchange x and y and solve for y

x = y^2 -10y

Complete the square

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

x+25 = (y-5)^2

Take the square root of each side

±sqrt(x+25) = y-5

Add 5 to each side

5±sqrt(x+25) = y

The inverse is 5±sqrt(x+25)

User Usman Javed
by
7.9k points

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