If g(x)is the inverse of f(x)andf(x)=4x+12,what is g(x)?
1 answer:
To find the inverse of a function, stick a y for the f(x).
So, f(x) = 4x + 12 becomes y = 4x + 12
Then switch the x and y.
So, y = 4x + 12 becomes x = 4y + 12
Then solve for y.
x = 4y + 12
x - 4y = 12 <-- Subtract both sides by 4y
-4y = 12 - x <-- Subtract both sides by x
y =
So, the inverse of f(x) is g(x) = -3 + x/4.
So, f(x) = 4x + 12 becomes y = 4x + 12
Then switch the x and y.
So, y = 4x + 12 becomes x = 4y + 12
Then solve for y.
x = 4y + 12
x - 4y = 12 <-- Subtract both sides by 4y
-4y = 12 - x <-- Subtract both sides by x
y =
So, the inverse of f(x) is g(x) = -3 + x/4.
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Answer:
Length of the flower garden = 29 meters
Width of the flower garden = 16 meters
Step-by-step explanation:
I have also attached a diagram for your convenience
Now First let us see the data we are given with:
Arif's backyard length = 37 meters
Arif's backyard Width = 24 meters
Area that should be left with grass = 424 m^2
Now lets suppose the width of the stirp of grass be "a"
According the image the area of backyard will be:
Area ABCD = 24 x 37
Area ABCD = 888 m^2
The length LM will be = (37 -2a)
The Width LO will be = (24 -2a)
Area LMNO = (37 -2a) x (24 -2a)
Area LMNO = 888 -74a -48a +4a^2
Area LMNO = 4a^2 -122a + 888
Now in order the to calculate the area of the grass strip we must subtract the area LMNO from the total area ABCD and we already know that the areas the area of grass strip should be 424 m^2
hence, A = Area ABCD - Area LMNO
424 = 888 - (4a^2 -122a + 888)
424 = 888 - 4a^2 +122a - 888
424 = -4a^2 +122a
4a^2 -122a +424=0
(We can solve this quadratic equation by breaking the middle term method)
2(2x-53)(x-4) = 0
2(2x-53) = 0
2x -53 = 0
x = 53/2
x = 26.5 (Not Possible)
x-4 = 0
x = 4
Length of the flower garden = 37 -2(4)
Length of the flower garden = 29 meters
Width of the flower garden = 24 -2(4)
Width of the flower garden = 16 meters
