need help with few questions

[mahi123]

hi please i have to hand my assignment in by tomorrow and i don't know how to get started on some of the questions

1) if f(x) = x^2 + 5, find f(x+1) - f(x)

I have no idea how to even begin here

2) Find the domains of the following functions.

a) f(x) = 2x-37, do we just find a value for which the equation equals zero so x can be any real number except that one?

3) divide 3a^2/ a^2 - b^2 by a/ a + b
thanks i really need help quickly with question 1 and 3

 

[Deleted member 4993]

hi please i have to hand my assignment in by tomorrow and i don't know how to get started on some of the questions

1) if f(x) = x^2 + 5, find f(x+1) - f(x)

find f(x+1) first...

f(x+1) = (x+1)^2 + 5....just replace (x) by (x+1)

then continue...

I have no idea how to even begin here

2) Find the domains of the following functions.

a) f(x) = 2x-37,

do we just find a value for which the equation equals zero ....No

find a value for which the function equals undefined ... like infinity


so x can be any real number except that one?

3) divide 3a^2/ a^2 - b^2 by a/ a + b

factorize a^2 - b^2

Then follow the principle of division by fraction

thanks i really need help quickly with question 1 and 3

 

[Loren]

1) if f(x) = x^2 + 5, find f(x+1) - f(x)

The letter "f" is telling you that there are a unique set of steps that are to be taken to execute that function. It is described by "x^2+5". That is telling you to take whatever is in the parenthesis in "f(x)" and square it, then add 5 to it. So, the function "f(x)" is defined as "square x then add 5 to that result." Now, as an example, if they were to give you "f(2x+3)" it would be telling you to square 2x+3 then add 5 to that result." So, given this example f(x)=x^2+5, f(2x+3)=(2x+3)^2 + 5 which equals 4x^2+12x+14. What this boils down to in your given problem is to simply replace all the x's in f(x)=x^2+5 with x+1 then subtract f(x) (which is x^2+5) and simplify. I got 2x+1.