Question

Inverse of a Function Help!

Answer 1

Which function below is the inverse of f(x) = x^2 − 9?

Answer 2

The answers have square roots, so I do not know how to solve this, please someone explain!

Answer 3

y = x^2 − 9. Now you have to express x in terms of y

Answer 4

do you mean switch the x and y variables?

Answer 5

sorry, I'm new to this, haha

Answer 6

\[y = x² - 9\]
\[y + 9 = x²\]
\[x = \sqrt{y + 9}\]

Answer 7

NO lets take a different example y= 2x+3 then inverse will be (y-3)/2

Answer 8

(1) write down y=f(x)

(2) switch x and y to get x=f(y)

(3) solve for y to get tex2html_wrap_inline48

Answer 9

this is the guide

Answer 10

where you see an \(x\) put a \(y\) and where you see a \(y\) put an \(x\)
it is just crutch, but it helps

Answer 11

suppose you had to solve
\[x^2-9=40\] for \(x\)
what would you do?

Answer 12

step one would be to add \(9\) to both sides to get \(x^2=49\) and step 2 would be to take the two square roots, \(x=\pm\sqrt{49}=\pm7\)

Answer 13

oh my goodness, haha. so many people, thanks everyone!

Satellite: So i use the square root whenever i have a variable with an exponent?

Answer 14

that is what the inverse function does
add 9, that the two square roots
\[\sqrt{x+9}\]

Answer 15

oops i meant \(\pm\sqrt{x+9}\)

Answer 16

yes

Answer 17

@official_snowflake if you want to solve \(x^2=whatever\) then the solution is \(\pm\sqrt{\text{whatever}}\)

Answer 18

but no, you don't always use the square root
you might need the cubed root, or the fourth root for example
depending on the exponent

Answer 19

oh oh oh okay. I get that!

Answer 20

btw i noticed you wrote in your question "which FUNCTION" below is the inverse of \(f(x)=x^2-9\) but did not include any answers

Answer 21

since the inverse requires \(\pm\) you see it is not a function

Answer 22

would you like the answer options?

Answer 23

for example, since both \(f(7)=40\) and \(f(-7)=40\) if w know only that \(f(x)=40\) we are not sure of what \(x\) is, it might be 7 or it might be -7
that means the inverse cannot be a function

Answer 24

the inverse function is

Answer 25

sure i would love to