Question

evaluate the attatched function

Answer 1

\[f(n)=n ^{3}+2; Find f(x-1)\]

Answer 2

there is no graph of a function. it only says write a direct variation function

Answer 3

@jim_thompson5910 a little help please?

Answer 4

wherever you see an 'n', replace it with 'x-1'

Answer 5

what do you get when you do this?

Answer 6

\[f(x-1)=(x-1)^{3}+2 \]
and then i got this \[f(x-1)= (x-1)(x-1)(x-1) +2 \]
and then i FOIL (x-1) and (x-1) but i dont know how to get the third

Answer 7

FOIL is great, but it's very limited (as you can see we hit a wall in this case)

I like to use the idea that

(A+B)(C+D) = A(C+D) + B(C+D)

and this idea can be extended as far as you want/need

Answer 8

(x-1)(x-1) = x(x-1) - 1(x-1)

(x-1)(x-1) = x^2-x - x +1

(x-1)(x-1) = x^2-2x +1

Answer 9

So

(x-1)(x-1)(x-1) +2

becomes

(x^2-2x +1)(x-1) +2

after we replace the first two (x-1) terms with x^2-2x +1

Answer 10

wouldn't it be x^2 +2x +1 (x-1) +2

Answer 11

now expand further and simplify

(x^2-2x +1)(x-1) +2

(x-1)(x^2-2x +1) +2

x(x^2-2x +1) - 1(x^2-2x +1) + 2 .... This is where the trick I showed above comes in handy

x^3-2x^2 +x - x^2+2x -1 + 2

x^3-3x^2 +3x + 1

Answer 12

oh nevermind, i think i see what i did wrong. i thought the 2x was positive

Answer 13

thanks i got it now ^^

Answer 14

yw