4-5

Last week we learned chapter 4 section 5. in 4-5 we learned about Inverses and how to determine the horizontal line test.

Horizontal line test- similar to the vertical line test only if it passes then there is an inverse that is a function

Sidenote-for our book they will say there isn’t an inverse if it fails

To find an inverse:

-Switch x & y

- solve for y

To check if something is an inverse:
F(g(x))=x
&
g(f(x))=x

-f^-1= inverse notation

Examples:

Prove f(x)=x+3 f^-1(x)=-x-3 are inverse

F(f^-1(X))=x-3+3=x

F^-1(f(X))
(x+3)-3=x

yes it is an inverse.

Y=square root of x-3

x=square root of y-3

square both side you get y-3=x^2
y^-1=x^2+3

it is an inverse because it passes the horizontal line test.


Basically if you know all these formulas and stuff section 4-5 will be easy for you.