Please help and show work with this problem.?

Question

If f(x)= 4 + 6x - x^4 , find f(a-2)

Answer 1

f(x) = 4 + 6x - x^4

Just substitute a - 2 for all x's
f(a - 2) = 4 + 6(a - 2) - (a - 2)^4

expand
f(a - 2) = 4 + 6a - 12 - (a^4 - 8a³ + 24a² - 32a + 16)

add
f(a - 2) = a^4 - 8a³ + 24a² - 26a + 8

^_^

Answer 2

What you are being asked here is to plug the term a-2 into the function like this,
f(x)= 4 + 6x - x^4
f(a-2)= 4 + 6(a-2) - (a-2)^4

Ask another question if you need help with the multiplication of the terms to get the final result.

Answer 3

Substitute (A-2) FOR x in f(x)= 4 + 6x - x^4 to get
f(a-2)= 4+6(a-2) -(a-2)^4

Fact is, if you can't simplify that expression, you best plan on taking algebra 1 over again.


Doug

Answer 4

Your first step is to replace x in the function everywhere it appears with (a-2). Then you multiply out the terms and simplify. You will need to use the binomial theorem to find the terms of (a-2)^4. After you do this, collect coefficients of like powers of a to simplify. You will get a result in the form Aa^4 + Ba^3 +Ca^2 + Da + E, where A,B,C,D,and E are your collected coefficients.

Answer 5

so, you put (a-2) everywhere you have x in the function...

f(x) = 4 + 6x - (a-2)^4
so
f(a-2) = 4 + 6(a-2) - (a-2)^4

= 4 + 6a - 12 - (a-2)^2*2
= 6a - 8 - (a^2 - 4a + 4)^2

...etc

Answer 6

remember, finding f(anything) always means sticking that "anything" in the function of f

so,

we have to stick (a-2) in the function described, an that would be:

f(a-2)=4+6*(a-2)-(a-2)^4

=4+6a-12-(a-2)^4
=-8+6a-(a-2)(a-2)(a-2)(a-2)
=-8+6a-[(a^2-4a+4)(a-2)(a-2)]
=-8+6a-[(a^3-4a^2+4a-2a^2+8a-8)(a-2)]
=-8+6a-a^4-4a^3+4a^2-2a^3+8a^2-8a-2a^3+8a^2-8a+4a^2-16a+16

what a mess

now round up the like terms and combine
=-8+16+6a-8a-8a-16a+4a^2+8a^2+8a^2+4a^2-4a^3-2a^3-2a^3-a^4
=8+6a+24a^2-8a^3

well, you did it
I do algebra for fun and you have worn me out

I expect I made at least one error getting to here, and now I can see that I don't want to go farther

I"m guessing I should do some trial and error with a term like (a+1) and see if I can get something to come out with long division

sounds like a job for the interested student, if we can find one

Answer 7

Does it specify what a is?? I think they just want to substitute all the x's with a-2. Therefore it would be:
4+6(a-2)-(a-2)^4

I hope this helps!

Answer 8

f(a - 2) means "replace "x" with "a - 2"


f(a - 2) = 4 + 6(a - 2) - (a - 2)^4

Then expand the expression:


4 + 6a - 12 - [ (a - 2)^2 * (a - 2)^2 ]

= 6a - 8 - [ (a^2 - 4a + 4) * (a^2 - 4a + 4) ]
= 6a - 8 - [ ((a^2 - 4a + 4)*(a^2) - (a^2 - 4a + 4)*(4a) + (a^2 - 4a + 4)*(4) ]
= 6a - 8 - [ (a^4 - 4a^3 + 4a^2) - (4a^3 - 16a^2 + 16a) + (4a^2 - 16a + 16) ]
= 6a - 8 - a^4 + 4a^3 - 4a^2 + 4a^3 - 16a^2 + 16a - 4a^2 + 16a - 16
= -a^4 + (4a^3 + 4a^3) + (- 4a^2 - 16a^2 - 4a^2) + (6a + 16a+ 16a) + (-8 -16)
= -a^4 + 8a^3 -24a^2 + 38a - 24

Answer 9

See my response to ANOTHER Algebra question....

:o)

I can't believe people actually take the time to solve these Algebra problems either....

Answer 10

f(a-2)= 4+69(a-2)-(a-2)^4
f(a-2)= 4+69a-138-(a-2)(a-2)(a-2)(a-2)
f(a-2)= 69a+134-(a^2-2a+4)(a-2)(a-2)
f(a-2)= 69a+134-(a^3-2a^2+4a-a^2+4a-8)(a-2)
f(a-2)= 69a+134-(a^3-3a^2+8a-8)(a-2)
f(a-2)= 69a+134-(a^4-3a^3+8a^2-8a-2a^3+6a^2- 16a+16)
f(a-2)= 69a+134-a^4-5a^3+14a^2-24a+16
f(a-2)= -a^4-5a^3+14a^2+45a+150