Question

Please help.. this is a tricky one! The one-to-one functions g and h are defined as follows: g={(-8,0), (-2,-4), (0,4), (6,5)} and h(x)=2x+3. Find the following: a) g^-1 (0) = ? b) h^-1 (x)=? c) (h^-1 º h)(-5)=?

Answer 1

I will give an example to illustrate the inverse function:
f(x) = x + 3
f(2) = 2 + 3 = 5
If f(2) = 5 it means f^-1(5) = 2

So for question a) which is g^-1 (0) = ?
Ask yourself what value of x makes g(x) = 0 ?

Answer 2

You are given: g(-8) = 0 ; g(-2) = -4 ; g(0) = 4 ; g(6) = 5
So for a) g( ? ) = 0 what should be in the place of the question mark?

Answer 3

Sorry I'm just out of it today.. lol. In the place of the question mark it should be -8. But I'm still confused... :/

Answer 4

Yes, g^-1 (0) = -8

Normally we are given the x value and we are asked to find the y.
In inverse function, we are given y and asked to find x.

Example: f(x) = x^2
We can put x = 1, 2, 3, etc. and calculate f(x) (or y values)
f(1) = 1^2 = 1 ==> f^-1(1) = 1
f(2) = 2^2 = 4 ==> f^-1(4) = 2
f(3) = 3^2 = 9 ==> f^-1(9) = 3

In the problem we are given a set of x, g(x)
g(-8) = 0 means g^-1(0) = -8
g(-2) = -4 means g^-1(-4) = -2
g(0) = 4 means g^-1(4) = 0
g(6) = 5 means g^-1(5) = 6

Answer 5

Yay.. I got the first part. How about the second part... that I reeeeeally don't understand

Answer 6

h(x) = 2x + 3. Find the inverse function h^-1(x)
Write the function as y = 2x + 3
To find the inverse function, switch x and y first. That is, put x in the place of y and y in the place of x. Then solve for y.
y = 2x + 3
Switch x and y
x = 2y + 3
Isolate y. To do that add -3 to both sides:
x - 3 = 2y
Divide both sides by 2
(x - 3) / 2 = y or
y = (x - 3) / 2 Therefore, the inverse function is:
h^-1(x) = (x - 3) / 2

Answer 7

Oh.. ok.. that makes some sense. Inversing is just confusing for me..

Answer 8

You practice with a few simple problems you will get the hang of it.

Answer 9

For the third part, (h^-1 º h)(-5)=?
means: find h^-1(h(-5))
The quickest answer is the h and its inverse h^-1 will cancel each other and leave just the -5 which is the answer.
But a longer version is: ......

Answer 10

(h^-1 º h)(-5) = h^-1(h(-5))
Find h(-5) first and whatever you find put it in the place marked "here"
h^-1( here ) and calculate h^-1(here).
h(x) = 2x + 3
Let us first find h(x) when x = -5
h(-5) = 2(-5) + 3 = -7
Therefore, h^-1(h(-5)) = h^-1(-7)
For part b) we found the inverse function:
h^-1(x) = (x - 3) / 2
h^-1(-7) = (-7 - 3) / 2 = -10 / 2 = -5

We arrived at the same conclusion earlier saying that in h^-1(h(-5)) the inverse function and the function will cancel each other out and leave you just with -5

Answer 11

Aww.. I see! I'm gonna try to practice some problems to see if I got it. Thanks sooo much for all your help and explanations!!!!!! Ure the best ;)

Answer 12

You are welcome.