SOLUTION: Find the inverse of f(x), where f(x)={{{x^2+4x+3}}}

Algebra ->  Rational-functions -> SOLUTION: Find the inverse of f(x), where f(x)={{{x^2+4x+3}}}      Log On


   

Question 1009988: Find the inverse of f(x), where f(x)=x%5E2%2B4x%2B3
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Find the inverse of f%28x%29, where f%28x%29=x%5E2%2B4x%2B3
recall f%28x%29=y, so you have
y=x%5E2%2B4x%2B3........swap x and y
x=y%5E2%2B4y%2B3.............solve for y
x=%28y%5E2%2B4y%2Bb%5E2%29-b%5E2%2B3..............complete square
x=%28y%5E2%2B4y%2B2%5E2%29-2%5E2%2B3
x=%28y%2B2%29%5E2-4%2B3
x=%28y%2B2%29%5E2-1
x%2B1=%28y%2B2%29%5E2
sqrt%28x%2B1%29=y%2B2
y=sqrt%28x%2B1%29-2
so, your inverse is
f%5E-1%28x%29=%28-2%2B-+sqrt%28x%2B1%29%29