Given $f (x) = x^{2} - 3 x$ $f(x)= x^2- 3x$ , how do you write the expression for $f (a + 2)$ $f(a+ 2)$ ?

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Answer 1 · 2017-01-06T13:12:17

$f (a + 2) = a^{2} + a - 2$ $f(color(red)(a + 2)) = a^2 + a - 2$

or

$f (a + 2) = (a + 2) (a - 1)$ $f(color(red)(a + 2)) = (a + 2)(a - 1)$

We will need to substitute $a + 2$ $color(red)(a + 2)$ for each occurrence of $x$ $color(blue)(x)$ in the original function.

$f (x) = x^{2} - 3 x$ $f(color(blue)(x)) = color(blue)(x)^2 - 3color(blue)(x)$

Becomes:

$f (a + 2) = {(a + 2)}^{2} - 3 (a + 2)$ $f(color(red)(a + 2)) = (color(red)(a + 2))^2 - 3(color(red)(a + 2))$

$f (a + 2) = ((a + 2) (a + 2)) - 3 a - 6$ $f(color(red)(a + 2)) = ((color(red)(a + 2))(color(red)(a + 2))) - 3a - 6$

$f (a + 2) = (a^{2} + 2 a + 2 a + 4) - 3 a - 6$ $f(color(red)(a + 2)) = (a^2 + 2a + 2a + 4) - 3a - 6$

$f (a + 2) = a^{2} + 2 a + 2 a + 4 - 3 a - 6$ $f(color(red)(a + 2)) = a^2 + 2a + 2a + 4 - 3a - 6$

$f (a + 2) = a^{2} + 2 a + 2 a - 3 a + 4 - 6$ $f(color(red)(a + 2)) = a^2 + 2a + 2a - 3a + 4 - 6$

$f (a + 2) = a^{2} + a - 2$ $f(color(red)(a + 2)) = a^2 + a - 2$

or

$f (a + 2) = (a + 2) (a - 1)$ $f(color(red)(a + 2)) = (a + 2)(a - 1)$

Given f(x)=x2−3xf(x)= x^2- 3x, how do you write the expression for f(a+2)f(a+ 2)?