Question

Someone please help?
Let f(x) = x2 – 16. Find f–1(x).

Answer 1

if we solve the problem:

y = x^2 - 16; for x, what does it look like?

Answer 2

and technically, there is no inverse function stated in the choices :/

Answer 3

I have no idea :(

Answer 4

we need to remember how to manipulate equation around to solve for a particular variable:

y = x^2 - 16

this can be algebrated about to solve for x

Answer 5

What would I do first?

Answer 6

would you agree that we can subtract 16 from each side to start to get x all alone?

Answer 7

err, add 16 to each side that is

Answer 8

Yes so it would be y = x^2/16? So C?

Answer 9

y = x^2 - 16
+16 +16
----------------
y+16 = x^2

its not C, I havent gotten to the end results yet .....

Answer 10

do you know how we can get the "^2" off the x?

Answer 11

Multiply it?

Answer 12

good attempt, but lets try to take the square root, or sqrt it

sqrt(y+16) = sqrt(x^2)

sqrt(y+16) = x

this is the general construct of our inverse function we are looking for, but they like to then swap xs and ys

Answer 13

Ohhhhh so it's B then?

Answer 14

B seems the most reasonable answer to me :)

Answer 15

Okay thank you! I have one more like this, could you help me with it too?

Answer 16

i can take a look at it sure

Answer 17

Let f(x) = 5x + 12. Find f–1(x).

Answer 18

lets try the same process, but this one is simpler since we aint got to sqrt nothing

y = 5x + 12

how do we solve for x so that x is all alone on one side of the equation?

Answer 19

- 12 from each side
y = 5x + 12
- 12 - 12
y - 12 = 5x

Answer 20

so far so good, now to uncover the x, we should divide off that pesky looking 5 right?

Answer 21

Yes so..
y - 12 = 5x
----------
5
y - 12/5 = x

Answer 22

I think I'm confusing myself

Answer 23

you did fine, lets just make sure its looks "proper" :)

\[\frac{y-12}{5}=x\]

Answer 24

Okay the closest choice I have to that is