SOLUTION: Consider the function f:R~R is given by x^2y+y=6. (1) find an explicit formula for f (2) what is the domain (3) state any three integer which are not in the range of f (4) ob

Algebra ->  Functions -> SOLUTION: Consider the function f:R~R is given by x^2y+y=6. (1) find an explicit formula for f (2) what is the domain (3) state any three integer which are not in the range of f (4) ob      Log On


   

Question 1189906: Consider the function f:R~R is given by x^2y+y=6.
(1) find an explicit formula for f
(2) what is the domain
(3) state any three integer which are not in the range of f
(4) obtain a formula for f^-1
(5) compute f^-1(5)
(6) For what value(s) of x is f^-1 undefined
(7) for what value(s) of x is f^-1 zero
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

(1)
x%5E2y%2By=6
%28x%5E2+%2B+1%29+y+=+6
y+=+6%2F%28x%5E2+%2B+1%29
y+=f%28x%29
f%28x%29=6%2F%28x%5E2+%2B+1%29

(2)
domain:
all real numbers: x element of R

(3) state any three integer which are not in the range of f
range: { f element R : 0+%3C+f+%3C=+6 }
any three integer which are not in the range: -1,0,7

(4) obtain a formula for+f%5E-1

f%28x%29=6%2F%28x%5E2+%2B+1%29.........y+=f%28x%29
y=6%2F%28x%5E2+%2B+1%29......swap variables
x=6%2F%28y%5E2+%2B+1%29...........solve for y
y%5E2+%2B+1=6%2Fx
y%5E2+=6%2Fx-1
y = ±sqrt%286%2Fx-1%29
f%5E-1=± sqrt%286+-+x%29%2Fsqrt%28x%29


(5) compute f%5E-1%285%29
f%5E-1%285%29=± sqrt%286+-+5%29%2Fsqrt%285%29= ±1%2Fsqrt%285%29=±sqrt%285%29%2F5


(6) For what value(s) of x is f%5E-1 undefined
if denominator equal to zero, so if x=0 then f%5E-1 will be undefined

(7) for what value(s) of x is f%5E-1 zero

0=± sqrt%286+-+x%29%2Fsqrt%28x%29
if numerator equal to zero, so
if x+=+6 then f%5E-1+=0