SOLUTION: For each function, graph the function and its inverse. If the inverse is a function, state the domain and range. a. f(x) = 2/(3 x) - 4 b. f(x) = 2x^2 -1 c. f(x) = 1/(x-1)

Algebra ->  Graphs -> SOLUTION: For each function, graph the function and its inverse. If the inverse is a function, state the domain and range. a. f(x) = 2/(3 x) - 4 b. f(x) = 2x^2 -1 c. f(x) = 1/(x-1)      Log On


   

Question 1186274: For each function, graph the function and its inverse. If the inverse is a function, state the domain and range.
a. f(x) = 2/(3 x) - 4
b. f(x) = 2x^2 -1
c. f(x) = 1/(x-1)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
a.
f%28x%29+=+2%2F%283+x%29+-+4
inverse
y+=+2%2F%283+x%29+-+4........swap variables
x+=+2%2F%283y%29+-+4........solve for y
x%2B4+=+2%2F%283y%29+
3y+=+2%2F%28x%2B4%29
y++=+2%2F%283%28x%2B4%29%29
f'%28x%29++=+2%2F%283%28x%2B4%29%29
Domain
{ x element R : x%3C%3E-4 }
Range
{ f%28x%29 element R : f%28x%29%3C%3E0 }



b.
f%28x%29+=+2x%5E2+-1
inverse
y+=+2x%5E2+-1
x+=+2y%5E2+-1
x%2B1+=+2y%5E2+
%28x%2B1%29+%2F2=y%5E2+
y=sqrt%28%28x%2B1%29+%2F2%29+
f'%28x%29= ± sqrt%28x+%2B+1%29%2Fsqrt%282%29
not a function



c.
f%28x%29+=+1%2F%28x-1%29
inverse
y+=+1%2F%28x-1%29
x=+1%2F%28y-1%29
%28y-1%29=+1%2Fx
y=+1%2Fx%2B1
f'%28x%29=1%2Fx%2B1
Domain
{ x+ element R : x%3C%3E0 }
Range
{ f%28x%29 element R+: f%28x%29%3C=1 }

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+1%2F%28x-1%29%2C1%2Fx%2B1%29+