Problem 1
<h3>Answer: False</h3>
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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.
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Problem 2
<h3>Answer: True</h3>
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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).
Answer:
y(-4) = 5
y'(-4) = -7
Step-by-step explanation:
Hi!
Since the tangent line T and the curve y must coincide at x=-4
y(-4) = T(-4) = 5
On the other hand, the derivative of the curve evaluated at -4 y'(x=-4) must be the slope of the tangent line. Which inspecting the tangent line T(x) is -7
That is:
y'(-4) = -7
Answer:
Ellie should have made 253$ in 23 hours in time. If she worked for 22 hours, then she made 242$.
Step-by-step explanation:
253$ / 11$= 23 hours
22 hours X 11$= 242 hours
Answer:
more, she uses 17.5 cups a week
Step-by-step explanation:
Answer:
c=7
Step-by-step explanation:
How to solve your problem
8=−3+29
8=−3c+298=-3c+298=−3c+29
Solve
1
Subtract
29
292929
from both sides of the equation
8=−3+29
8=−3c+298=-3c+298=−3c+29
8−29=−3+29−29
8−29=−3c+29−298{\color{#c92786}{-29}}=-3c+29{\color{#c92786}{-29}}8−29=−3c+29−29
2
Simplify
3
Divide both sides of the equation by the same term
4
Simplify
Solution
=7
Hope this helps!
Have a great day!
-Lea
