Question

The one-to-one functions "g" and "h" are defined as follows.

g = {(-4,1), (1,-9), (5,-4), (8,3)}
h(x) = 3x + 14

Find the following:

g^-1 (1)

(h^-1 o h)(-2)

Answer 1

Any function to the power of -1 is the inverse of the original function. So first find the function for g and then inverse it. You can get the function by comparing the x and y values. Is that hint enough?

Answer 2

How do I find the function for g?

Answer 3

Well one way is to look at the x and y values you have. A function is something that transforms (usual notations) x to y. So take a look at the set. How can you turn -4 to 1. The same method should turn 1 to -9, 5 to -4, and 8 to 3.

Answer 4

Well that doesn't seem to be the case right away with the four common methods (addition, subtraction, multiplication, division)

Answer 5

A second method might be to plot a graph using those points and then obtain the line's equation in the form of y = bx + c

Answer 6

I've gathered that it has to be a parabola. How do I go from there?

Answer 7

Waitaminit... DUHHH. It asks for g^-1 for x = 1. They gave you what g is when x = 1. So just inverse that.

Answer 8

So y should be -9 for the first one?

How do I do the second one?

Answer 9

-9 is when it is g(x) so the inverse should be -1/9 I believe. For the second one you will have to invert the function first then put in x = -2. This might help: http://www.purplemath.com/modules/invrsfcn3.htm

Answer 10

Orrrrr the first one is 9. I'm sorry I just haven't done this in years. You might wanna check on inverse function identities or something.

Answer 11

OK

Answer 12

for g^-1 (1), look at the point where y=1..
finding the point of an inverse function given a point of function is simply switching the values of x and y..

Answer 13

for example the function has a point (3, -1), the inverse function will have the point (-1, 3)..
we are just simply switching the values of x and y..

Answer 14

@timhaag1 did you get what i mean?

Answer 15

Yes! I understand the first part. But how do I find the part involving h?

Answer 16

@Data_LG2 Yes! I understand the first part. But how do I find the part involving h?

Answer 17

same thing as you did with g, the difference is you need to switch x and y in the equation and arrange the equation in terms of y..

Answer 18

Wait is the answer to the first part -4 or -9? Because y should be -1 in this case if it is the inverse so the answer should be

Answer 19

you are given: (-4,1), (1,-9)
g(x)
g(1)=-9
g^-1(1)= -4

Answer 20

Good

Answer 21

Is the second answer -2?

Answer 22

i need to explain it faster i need to go now..