SOLUTION: In equation is Find a formula for F^-1(x). Give domain of f^-1 , including restrictions from f. 17.F(x)= sqrt(x-3) 21. f(x)= 3sqrt(x+5)?

Algebra ->  Rational-functions -> SOLUTION: In equation is Find a formula for F^-1(x). Give domain of f^-1 , including restrictions from f. 17.F(x)= sqrt(x-3) 21. f(x)= 3sqrt(x+5)?      Log On


   

Question 1049492: In equation is Find a formula for F^-1(x). Give domain of f^-1 , including restrictions from f. 17.F(x)= sqrt(x-3) 21. f(x)= 3sqrt(x+5)?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=+sqrt%28x-3%29+
since f%28x%29=+y we have
y=+sqrt%28x-3%29+.........swap x+and y
x=+sqrt%28y-3%29.........solve for+y, first square both sides
x%5E2=+%28sqrt%28y-3%29%29%5E2
x%5E2=+y-3
x%5E2%2B3=+y
so, f%5E-1%28x%29=x%5E2%2B3

domain: R (all real numbers)

f%28x%29=+3sqrt%28x%2B5%29
y=+3sqrt%28x%2B5%29........swap x+and y
x=+3sqrt%28y%2B5%29......solve for+y, first square both sides
x%5E2=+%283sqrt%28y%2B5%29%29%5E2
x%5E2=+9%28y%2B5%29
x%5E2%2F9=+y%2B5
%281%2F9%29x%5E2-5=+y
f%5E-1%28x%29=%281%2F9%29x%5E2-5
domain: R (all real numbers)