# Thread: Problem with solving function

1. ## Problem with solving function

I have problem solving function with definition
$\displaystyle f:[1,\infty)\rightarrow \mathbb{R}$
$\displaystyle f(x^2+1)=\vert x\vert + 2 x^2 + x^4$
for these two
$\displaystyle f(5)\ and\ f(x)$

im very lost...

2. $\displaystyle f(x^2+1)=\vert x\vert + 2 x^2 + x^4$

$\displaystyle = \vert x^2+1\vert + 2 x^2 + x^4$

since $\displaystyle x^2$ will always be positive then
$\displaystyle x^2+1 + 2( x^2+1)^2 +( x^2+1)^4$
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$\displaystyle f(5)=\vert 5\vert + 2 x^2 + x^4 = 5 +2(5)^2 + (5)^4 = 680$

3. Originally Posted by bigwave
$\displaystyle f(x^2+1)=\vert x\vert + 2 x^2 + x^4$

$\displaystyle = \vert x^2+1\vert + 2 x^2 + x^4$

since $\displaystyle x^2$ will always be positive then
$\displaystyle x^2+1 + 2 x^2 + x^4$

combine like terms

$\displaystyle x^4 + 3x^2 + 1$

this will factor using the quadradic equation but may not need to do this

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$\displaystyle f(5)=\vert 5\vert + 2 x^2 + x^4 = 5 +2(5)^2 + (5)^4 = 680$
But why you didnt insert $\displaystyle x^2+1$ in to other $\displaystyle x$ es

4. you are correct
sorry i missed that
makes it more complicated....
i corrected it in the first reply