Question

Can anyone please help to let me know if I am solving this the right way?
f(x) = x^4 + 5, g(x) = x - 4 and h(x) = sqrt(x)
f(g(h(x))) = h(x) = sqrt(x) = g(sqrt(x)) = sqrt(x-4)...

Answer 1

I have to find f(g(h(x)))

Answer 2

no your plugging in gx into hx but ur suppose to plug in hx into gx

Answer 3

yeah there is a lot of variables and so I am getting confused

Answer 4

yeah its reasonable but u had the right idea just plug in the function of h(x) for every x you see in g(x)

Answer 5

h(x)= sqrt(x) = g(x) = x - 4?

Answer 6

its asking you to plug in hx into gx or (g(hx)) so... sqrtx-4 now try the next part

Answer 7

(sqrtx)-4 the 4 is outside the sqrt

Answer 8

so you keep working backwards starting with h(x) and then g(h(x)) and then f(g(h(x)))?

Answer 9

if

\[h(x) = \sqrt{x}\]

then

\[g(h(x)) = g(\sqrt{x}) = \sqrt{x} - 4 \]

so for

f(g(h(x)))

in f(x) replace x with

\[\sqrt{x} - 4\]

hope it helps

Answer 10

where does the x^4+5 come in for f(x)?

Answer 11

ok... so replacing x with

\[\sqrt{x} - 4\]

its

\[f((g(h(x))) = f(\sqrt{x} -4) = (\sqrt{x} - 4)^4 + 5\]

Answer 12

there is a lot of substation in a problem like this

Answer 13

I did some problems before this that were just f(g(x)) but it got more complicated with f(g(h(x)))

Answer 14

its a tough problem.... probably at the top end of questions...

Answer 15

ok, so I put in f(g(h(x))) = (sqrt(x-4)^4 + 5) and still got it incorrect

Answer 16

is that because we need to simplify?

Answer 17

I'd say so.... you need to expand it....

I'd suggest you look at wolfram alpha and get it so simplify it

Answer 18

I will put it into wolfram alpha

Answer 19

yep just go simplify (sqrt(x) - 4)^4 + 5

then enter

it should work

Answer 20

ok wolfram alpha came back with (x-4)^2 + 5

Answer 21

still not right... looking at the problem again

Answer 22

well this is what I have

\[x^2 - 16\sqrt{x^3} + 96x -256\sqrt{x} + 261\]

Answer 23

ok let me plug that in

Answer 24

that was it... can you walk me through it now? that would be extremely helpful

Answer 25

I have an exam on tuesday

Answer 26

@campbell_st

Answer 27

well you have

\[(\sqrt{x} - 4)^2 \times (\sqrt{x} -4)^2 + 5\]

so I distributed and got

\[(x - 8\sqrt{x} + 16) \times (x - 8\sqrt{x} + 16)\]

then its a very tedious process of

\[x(x - 8\sqrt{x} + 16) - 8\sqrt{x}(x - 8\sqrt{x} + 16)+ 16(x - 8\sqrt{x} + 16) + 5\]

etc etc ... hope it makes sense...

Answer 28

wow... that is a lot of work

Answer 29

is there not a faster way to do the problem? I am bound to make and error doing all that work

Answer 30

well you could use binomial expansion....

the coefficients are

1 4 6 4 1 from pascals triangle

\[(\sqrt{x} - 4) = 1 \times (x^{\frac{1}{2}})^4 \times (-4)^0 + 4 \times (x^{\frac{1}{2}})^3 \times (-4)^1 + ... \]

the powers of x decrease and the powers of (-4) increase

Answer 31

oh my instructor mentioned pascal's triangle in class but I don't even know that concept so that is out of the question...

Answer 32

never been introduced to pascal's triangle

Answer 33

maybe for now the long way is my only choice

Answer 34

I'd say so... I'd expect its a very unfair examination question... just because of the amout of time needed to get a solution

Answer 35

yeah, I'd agree with that... so for now in my homework I will put the tedious work down so at least it shows I made an effort to get to the solution