Question

Let, $f(x+1)=2x^2-3x-1$, then find the value of $f\left(0\right)$ and $f(x+2)$.

Answer 1

Given,$f(x+1)=2x^2-3x-1$......(1).

Putting $x=-1$ in the above expression we get,

$f\left(0\right)=2.(-1{)}^2-3.(-1)-1$

or, $f\left(0\right)=4$.

Now putting $x+1$ in expression (1) in stead of $x$ we get,

$f(x+2)=2(x+1{)}^2-3(x+1)-1=2x^2+x-2$