## anonymous 4 years ago Explain what do you mean by a one to one funtion? b) Explain briefly in steps how you would determine the inverse of a function f(x) c) Find the inverse of the function f(x)= x-1 the x-1 is in the square root formation

1. anonymous

a) as i think , I'm not sure .. each value of x gives one value to y and each value of y gives one value of x . b) solution is ... Put x on one side and y on the other side of equation .. and to make the function details by y only c) f(x)=(x−1)2 y=(x−1)2 take root for both sides √y=(x−1) Put x on part and y on the other part .. and to make the function details by y only. x=√y+1

2. precal

I believe the originial function is $f(x)=\sqrt{x-1}$ to find the inverse rewrite as $y=\sqrt{x-1}$ switch the x and y $x=\sqrt{y-1}$ Solve for y $x=\sqrt{y-1}$ $\left( x \right)^2=\left( \sqrt{y-1} \right)^2$ x=y-1 add 1 to both sides x+1=y your inverse is $f \left( x \right)^{-1}=x+1$

3. anonymous

$f^{-1}(x)=x^2+1\quad,\quad x\ge 0$

4. anonymous

NikVist ? how you Find that answer ?

5. precal

yes I am sorry. You are correct in correcting my last step I dropped the 2nd power all of my steps are correct. $x^2=y-1$ add 1 to both sides $x^2+1=y$ This is the inverse $f \left( x \right)^{-1}=x^2+1$