SOLUTION: Find the equation of the inverse for each function. State which of the following inverses are functions. a. f(x) = 1/(2 x) - 3 b. f(x) = 4x 2 - 5 c. A(r) = 4(Pi)r^2

Algebra ->  Functions -> SOLUTION: Find the equation of the inverse for each function. State which of the following inverses are functions. a. f(x) = 1/(2 x) - 3 b. f(x) = 4x 2 - 5 c. A(r) = 4(Pi)r^2      Log On


   

Question 1186231: Find the equation of the inverse for each function. State which of the following inverses are functions.
a. f(x) = 1/(2 x) - 3
b. f(x) = 4x 2 - 5
c. A(r) = 4(Pi)r^2
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

a. f%28x%29+=+1%2F%282x%29+-+3
f%28x%29+=+y
y+=+1%2F%282x%29+-+3...........swap variables
x=+1%2F%282y%29+-+3.........solve for y
x%2B3=+1%2F%282y%29+
2y=+1%2F%28x%2B3%29+
y=+1%2F%282%28x%2B3%29%29+

=> f'%28x%29+=+1%2F%282%28x%2B3%29%29+


b. f%28x%29+=+4x%5E2+-+5
y=+4x%5E2+-+5
x=+4y%5E2+-+5
x%2B5=+4y%5E2+
%28x%2B5%29%2F4=+y%5E2+
y= ± sqrt%28%28x%2B5%29%2F4%29+
f'%28x%29= ± sqrt%28x+%2B+5%29%2F2


c. A%28r%29+=+4%28Pi%29r%5E2
r+=+4%28Pi%29%28A%28r%29%29%5E2.........swap variables
r%2F4%28Pi%29=%28A%28r%29%29%5E2
A'%28r%29= ± sqrt%28r%29%2F%282sqrt%28pi%29%29