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# If f(x)=x^2 + 2x +3, then how do you find f(a-1)?

May 28, 2016

${a}^{2} + 2$

#### Explanation:

Substitute x = a-1 into function.

$\Rightarrow f \left(a - 1\right) = {\left(a - 1\right)}^{2} + 2 \left(a - 1\right) + 3$

expand brackets and collect like terms.

$\Rightarrow {\left(a - 1\right)}^{2} + 2 \left(a - 1\right) + 3 = {a}^{2} - 2 a + 1 + 2 a - 2 + 3$

$= {a}^{2} + 2$

May 28, 2016

It is enough to substitute $x$ with $\left(a - 1\right)$.

#### Explanation:

It is enough to write $\left(a - 1\right)$ every time that you read $x$.

$f \left(a - 1\right) = {\left(a - 1\right)}^{2} + 2 \left(a - 1\right) + 3$

then it is just a matter of doing a bit of algebra

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