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• Function: f(x) = 3x + 12.
A. Finding the inverse of f.
The composition of f with its inverse results in the identity function:
(f o g)(x) = x
f[ g(x) ] = x
3 · g(x) + 12 = x
3 · g(x) = x – 12
x – 12
g(x) = ⸺⸺
3
x g(x) = ⸺ – 4 <——— this is the inverse of f.
3________
B. Verifying that the composition of f and g gives us the identity function:
•
and also
•
________
C. Since f and g are inverse, then
f(g(– 2))
= (f o g)(– 2)
=
– 2 <span>✔
</span>
• Call h the compositon of f and g. So,
h(x) = (f o g)(x)
h(x) = x
As you can see above, there is no restriction for h. Therefore, the domain of h is R (all real numbers).
I hope this helps. =)
Answer: Hence, our required model will be
Explanation:
Since we have given that
Luana bought a new phone and
For 3 months, the amount she paid = $175
For 6 months, the amount she paid = $295
Now, we have to model an equation ,
Here, let cost be 'C' and
Let number of months be 'm'.
So, we will use the "equation of line" i.e. for two point slope form :
Here y represented by 'C' and x represented by 'm'
So,
Hence, our required model will be
If r = -3 and s = 5:
(r^-4)(s^2) = (-3^-4)(5^2) = (1/81)(25) = 25/81
If r = 5 and s = -3:
(r^-4)(s^2) = (5^-4)(3^2) = (1/625)(9) = 9/625
The slope of the line in the table given is 11
<h3>Slope of a Line</h3>
In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate.
The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.
Hence, the change in y-coordinate with respect to the change in x-coordinate is given by
m = y₂ - y₁ / x₂ - x₁
Taking two points from the table
m = 1172 - 864 / 72 - 44
m = 11
The slope of the line is 11
Learn more on slope of a line here;
brainly.com/question/16949303
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