Question

if f(x+2) = x² - 6x +2 then f(0) = ?​

Answer 1

$\bigstar$ Explanation $\bigstar$

$\leadsto$ Given:-

$f(x+2) = x^2 - 6x + 2$

$\leadsto$ Solution:-

We need to find f(0) but we can't just put the value x = 0.

Therefore,

We need to find the value of x when x + 2 = 0

$x + 2 = 0 \implies x = -2$

We have found the value of x so we can put the value of x in f(x+2)

Therefore,

f(0) = $(-2)^2 - 6(-2) + 2\implies 4 +12 +2 = 18$

$\boxed{Answer\:is\:18}$

$\leadsto$ Reason we didn't put value of x = 0 in f(x+2) to find f(0)

Let us consider a polynomial,

$g(x) = ax^2 + bx+c$

If we want to find g(0),

Then,

We can directly put the value of x as 0,

But here we are indirectly equating x to 0.

This is the same thing we have done to find the solution.