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

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Answer 1 · 2017-01-06T13:12:17

#f(color(red)(a + 2)) = a^2 + a - 2#

or

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

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

#f(color(blue)(x)) = color(blue)(x)^2 - 3color(blue)(x)#

Becomes:

#f(color(red)(a + 2)) = (color(red)(a + 2))^2 - 3(color(red)(a + 2))#

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

#f(color(red)(a + 2)) = (a^2 + 2a + 2a + 4) - 3a - 6#

#f(color(red)(a + 2)) = a^2 + 2a + 2a + 4 - 3a - 6#

#f(color(red)(a + 2)) = a^2 + 2a + 2a - 3a + 4 - 6#

#f(color(red)(a + 2)) = a^2 + a - 2#

or

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