can someone show me how to do this? o.O

f(x)=x^2+4
f(x+1)-f(1)

Question

can someone show me how to do this? o.O

f(x)=x^2+4
f(x+1)-f(1)

anonymous · Answer

sub the expression x+1 into the variable in the function, and then subtract from that the function with 1 subbed in for the variable

anonymous · Answer

F(x+1)-F(x)=(x+1)^2+4 - [1^2+4] and then simplify

anonymous · Answer

ohhh ok

anonymous · Answer

=x^2+2x+1+4-5=x^2+2x

anonymous · Answer

how do i do it with a fraction?
$$f(x-5)-f(x)/5$$

anonymous · Answer

function is defined by the same rule?

anonymous · Answer

just divide the function by 5, e.g., 
$$(x-5)^2+4-\frac{x^2+4}{5}=...$$now simplify

anonymous · Answer

$$=x^2-10x+25+4-\frac{1}{5}x^2+\frac{4}{5}=\frac{4}{5}x^2-\frac{46}{5}x+4$$

anonymous · Answer

ok thanks

anonymous · Answer

wait, the constant of 4 should be 29 (as in 25+4); sorry someone was talking to me as I was finishing your solution.

anonymous · Answer

no wait-- its worse than that give a a minute to fix this

anonymous · Answer

ok

anonymous · Answer

$$=\frac{4}{5}x^2-10x+29+\frac{4}{5}=\frac{4}{5}x^2-10x+29+\frac{145}{5}+\frac{4}{5}$$$$=\frac{4}{5}x^2-10x+\frac{149}{5}$$this is the correct one (I hope!)

anonymous · Answer

is that simplified?

anonymous · Answer

yes there are no more like terms, and i think i got it right this time