Question

help:) f(x) = 3x-1
g(x)= 5/2x+7
h(x)= x^2+1

find:
(f•g•h)(x)

Answer 1

is that the composition symbol?

Answer 2

(f•g•h)(x) = f( g( h(x)))

Answer 3

try this notation f(g(h(x)))

Answer 4

first find fg then subs h in place of x u will get fg(h(x))

Answer 5

I work from inside to outside...so i start with g(h(x))...this means take the funciton h(x) and use it as the input into g(x).

Answer 6

\[g(h(x)) = \frac{5}{2(x^{2}+1)+7}=\frac{5}{2x^{2}+9}\]

Answer 7

yah, i get that part:)

Answer 8

Now, use this as the input into f(x)

Answer 9

note i'm assuming its 5/2 * x

Answer 10

:) SO where are you lost?

Answer 11

with my final ans.

Answer 12

\[3( 5/2 * (x^2 +1 ) +7 ) +1\]

Answer 13

I get \[\frac{15}{2x^{2}+9}-1\]as my final anwer. :)

Answer 14

based on the previous problems, we used \[g(x)=\frac{5}{2x+7}\]

Answer 15

i get that too:)

Answer 16

am i not going to perform the indicated operation 2 subtract it from 1

Answer 17

See, you don't need our help :)

Answer 18

I wouldn't. The answer is correct and simplified.

Answer 19

Anything more is complicating it more than it needs.

Answer 20

If you were to do that, you'd have to make the 1 into the quadratic on the bottom and then do the subtraction in the numerator.

Answer 21

That would give you x terms in both top and bottom whereas now you only have them on the bottom...much prettier :)

Answer 22

so, its better not to subtract it anymore?

Answer 23

much better not to.

Answer 24

A commented Mathematica solution is attached.