For a given function f(x) we define the domain restrictions as values of x that we can not use in our function. Also, for a function f(x) we define the inverse g(x) as a function such that:
g(f(x)) = x = f(g(x))
<u>The restriction is:</u>
x ≠ 4
<u>The inverse is:</u>
Here our function is:
We know that we can not divide by zero, so the only restriction in this function will be the one that makes the denominator equal to zero.
(x - 4)^2 = 0
x - 4 = 0
x = 4
So the only value of x that we need to remove from the domain is x = 4.
To find the inverse we try with the general form:
Evaluating this in our function we get:
Remember that the thing above must be equal to x, so we get:
From the two above equations we find:
b = 11
a = 4
Thus the inverse equation is:
If you want to learn more, you can read:
brainly.com/question/10300045
The red line is a reflection across the x-axis, so the correct option is d.
<h3>
How to write the equation for the red line?</h3>
First, we know that the black line is represented by y = f(x). Here, we can see that the red line is given by a reflection around the x-axis.
This reflection only changes the sign of the right side, then we get that the function of the red line is:
g(x) = -f(x)
Then we can write this as:
y = g(x) = -f(x) = -1*f(x)
If we divide both sides by -1, we get:
y/(-1) = f(x)
Like in option d, so that is the correct one.
If you want to learn more about reflections:
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Answer:
Length is 20 m and width is 4 m.
Step-by-step explanation:
Given:
Perimeter of the rectangular alley, 
Length is 5 times the width.
Let width be 
.
So, as per question,
Length,
Now, perimeter of rectangle is given as:
Plug in 48 for 
, 
for 
and for b.
Therefore, width is 4 m.
Length is 
m.
Answer:
Reindeer runs in 3 hrs = 20×1/4 miles
Reindeer runs in 1 hr = 81/4 × 1/3 = 6 × 3/4 miles (option 2)
Answer:
480
Step-by-step explanation:
because 120×4=480 if im correct
