SOLUTION: Determine if the following function has an inverse function. k(x)=3x^2−5 A. k has an inverse function B. k does NOT have an inverse function

Algebra ->  Inverses -> SOLUTION: Determine if the following function has an inverse function. k(x)=3x^2−5 A. k has an inverse function B. k does NOT have an inverse function      Log On


   

Question 1187100: Determine if the following function has an inverse function.
k(x)=3x^2−5
A. k has an inverse function
B. k does NOT have an inverse function
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

k%28x%29=3x%5E2-5
find inverse:
recall that
k%28x%29=y
y=3x%5E2-5.........swap variables
x=3y%5E2-5.........solve for+y
x%2B5=3y%5E2
y%5E2=%28x%2B5%29%2F3
y=sqrt%28x%2B5%29%2F3%29
+y= ± sqrt%28x+%2B+5%29%2Fsqrt%283%29
=> inverse is k'%28x%29= ± sqrt%28x+%2B+5%29%2Fsqrt%283%29

A. k has an inverse function