Problem 1
<h3>Answer: False</h3>
---------------------------------
Explanation:
The notation (f o g)(x) means f( g(x) ). Here g(x) is the inner function.
So,
f(x) = x+1
f( g(x) ) = g(x) + 1 .... replace every x with g(x)
f( g(x) ) = 6x+1 ... plug in g(x) = 6x
(f o g)(x) = 6x+1
Now let's flip things around
g(x) = 6x
g( f(x) ) = 6*( f(x) ) .... replace every x with f(x)
g( f(x) ) = 6(x+1) .... plug in f(x) = x+1
g( f(x) ) = 6x+6
(g o f)(x) = 6x+6
This shows that (f o g)(x) = (g o f)(x) is a false equation for the given f(x) and g(x) functions.
===============================================
Problem 2
<h3>Answer: True</h3>
---------------------------------
Explanation:
Let's say that g(x) produced a number that wasn't in the domain of f(x). This would mean that f( g(x) ) would be undefined.
For example, let
f(x) = 1/(x+2)
g(x) = -2
The g(x) function will always produce the output -2 regardless of what the input x is. Feeding that -2 output into f(x) leads to 1/(x+2) = 1/(-2+2) = 1/0 which is undefined.
So it's important that the outputs of g(x) line up with the domain of f(x). Outputs of g(x) must be valid inputs of f(x).
3(2y-3)=27
6y-9=27
6y=36
y=6
Answer:
<em>The slope of the line is -1</em>
Step-by-step explanation:
<u>Slope of a Line</u>
Suppose we know a given line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated as follows:
From the table in the image, we select the points (1,4) (3,2). The slope is:
Now select two other points like (5,0) (7,-2)
Following the same procedure with any other pair of points, we'll get the very same result:
The slope of the line is -1
Answer:
1 7/8 quarts
Step-by-step explanation:
The amount Yuan has left can be found by multiplying the original amount by the fraction he has left.
__
<h3>used</h3>
After using 1/2 of the broth for soup, the fraction remaining is ...
1 -1/2 = 1/2
The amount Yuan used for gravy is 1/4 of this, or ...
(1/4)(1/2) = 1/8 . . . of the original amount of broth
The total fraction Yuan used was ...
fraction used = fraction for soup + fraction for broth = 1/2 +1/8 = 5/8
<h3>remaining</h3>
Then the fraction remaining is ...
fraction remaining = 1 - fraction used = 1 - 5/8 = 3/8.
The amount remaining is this fraction of the original amount:
(3/8)(5 quarts) = 15/8 quarts = 1 7/8 quarts . . . . remaining
Hi,
It is unlikely that the game show contestant will win the boat.
To be exact it is 20% chance that the game show contestant will win the boat.
XD
