Answer:
a = 4.762203156
Step-by-step explanation:
Given:
ab^4 = 12 and a^5b^5 = 7776
Making the equations a subject of a;
a = 12/b^4 and a^5 = 7776/b^5
Finding fifth root on both sides of equation two;
a = /b
You will get a = 6/b
Equating the two equations;
12/b^4 = 6/b
Multiplying both sides by b^4 gives:
b = = 1.25992105
We had that a = 12/b^4 so;
a = 12/1.25992105^4 = 12/2.5198421 = 4.762203156
Answer:
Step-by-step explanation:
First, let's change those variables to x and y, just for the sake of convenience. In order to find the inverse of a function algebraically, switch the x and y coordinates, then solve for the new y. Letting y = A(n) and x = n (we will switch them back when we're done):
y = 3x - 20. This is linear; a line with a slope of 3 and a y-intercept of -20. When we switch the x and the y, we get:
x = 3y - 20. Now we solve for the new y. Begin by adding 20 to both sides:
x + 20 = 3y. Now divide both sides by 3:
, or to write it in slope-intercept form, like the function you started with:
This is also a line, with a slope of 1/3 and a y-intercept of +20/3
Now, replacing:
That is how to write the inverse using function notation. The little -1 as an exponent tells us that this is the inverse of the function A(n).