SOLUTION: Find the inverse of each function. Is the inverse a function? f(x)=3x+2 f(x)=x^2-5

Algebra ->  Rational-functions -> SOLUTION: Find the inverse of each function. Is the inverse a function? f(x)=3x+2 f(x)=x^2-5      Log On


   

Question 186434: Find the inverse of each function. Is the inverse a function?


f(x)=3x+2
f(x)=x^2-5
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the inverse of each function. Is the inverse a function?
-----
f(x)=3x+2
Interchange x and y to get:
x = 3y + 2
Solve for y
y = (1/3)x-(2/3)
Yes, it is a function
---------------------
Graph of the function and its inverse:
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C3x%2B2%2C%281%2F3%29x-%282%2F3%29%29
==============================
f(x)=x^2-5
Interchange:
x = y^2 -5
Solve for y:
y^2 = x+5
y = +sqrt(x+5) ; y = -sqrt(x+5)
No, it is not a function
------------------------------
Graph of the function and its inverse:

---------------------------------------------
Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given function.


Replace f(x) with 'y'


Switch x and y


Subtract 2 from both sides.


Divide both sides by 3


Rearrange the equation.



So the inverse function is which is a function.




-------------------------------------------------------------------


Start with the given function.


Replace f(x) with 'y'


Switch x and y


Add 5 to both sides.


Rearrange the equation


Take the square root of both sides. Note: don't forget the "plus/minus"


or Break up the "plus/minus" to form two separate equations.


Since we have two separate equations, this means that we CANNOT write the inverse as one function.


So the inverse is NOT a function.