$\displaystyle f : R-> R$
$\displaystyle f(x)= x^{2}+2x+3$
a) Define a restriction of $\displaystyle f$ that admits inverse.
Can u help me ?? I dont have any idea, how to do that.
$\displaystyle f : R-> R$
$\displaystyle f(x)= x^{2}+2x+3$
a) Define a restriction of $\displaystyle f$ that admits inverse.
Can u help me ?? I dont have any idea, how to do that.
I already know the inverse function.
$\displaystyle x = +/-\sqrt{y-2}-1$
The inverse graph is a parabole with vertex(2,-1)
I dont understood the part f(x) is 1-1
btw: Sorry for posting in wrong section(this problem is from a university calculus test)
A function is 1-1 (or injective) if it maps different arguments to different values. For a function to have an inverse, it must be injective: if $\displaystyle y = f(x_1) = f(x_2)$ where $\displaystyle x_1\ne x_2$, then $\displaystyle f^{-1}(y)$ is not defined because it cannot be both $\displaystyle x_1$ and $\displaystyle x_2$. Therefore, you need to find a restriction where the function is 1-1, as skeeter said.