Question

Given the following: f(x)=3x^\frac12+7x^{-\frac14}+8x^{-4};\;f(x)=3x
2
1
​

+7x
−
4
1
​

+8x
−4
; g(x)=-\frac74x^\frac12+12x^{-\frac14}-21x^3;\;and\;g(x)=−
4
7
​
x
2
1
​

+12x
−
4
1
​

−21x
3
;and h(x)=8x^3+12x^{-\frac12}+6x^\frac14-14x^{-4}h(x)=8x
3
+12x
−
2
1
​

+6x
4
1
​

−14x
−4

Complete the following: g(x)-h(x)g(x)−h(x)


-29x^3-\frac74x^\frac12+6x^{-\frac14}-12x^{-\frac14}\;-12x^{-\frac12}+14x^{-4}−29x
3
−
4
7
​
x
2
1
​

+6x
−
4
1
​

−12x
−
4
1
​

−12x
−
2
1
​

+14x
−4


29x^3-\frac74x^\frac12-6x^{-\frac14}+12x^{-\frac14}\;-12x^{-\frac12}+14x^{-4}29x
3
−
4
7
​
x
2
1
​

−6x
−
4
1
​

+12x
−
4
1
​

−12x
−
2
1
​

+14x
−4


-29x^3-\frac74x^\frac12-6x^\frac14+12x^{-\frac14}\;-12x^{-\frac12}+14x^{-4}−29x
3
−
4
7
​
x
2
1
​

−6x
4
1
​

+12x
−
4
1
​

−12x
−
2
1
​

+14x
−4


-29x^3-\frac74x^\frac12-6x^{-\frac14}+12x^{-\frac14}\;-12x^{-\frac12}-14x^{-4}−29x
3
−
4
7
​
x
2
1
​

−6x
−
4
1
​

+12x
−
4
1
​

−12x
−
2
1
​

−14x

−4

Answer 1

have you edit the question before posting it? pls retype this and i’ll be back to help you out.

Answer 2

The value of the composite function g(x)- h(x) is $-29x^3-\frac74x^\frac12-6x^\frac14 +12x^{-\frac14}-12x^{-\frac12}+ 14x^{-4}$

How to complete the functions?

The functions are given as:

$f(x)=3x^\frac12+7x^{-\frac14}+8x^{-4$

$g(x)=-\frac74x^\frac12+12x^{-\frac14}-21x^3$

$h(x)=8x^3+12x^{-\frac12}+6x^\frac14-14x^{-4}$

The value of the function g(x) - h(x) is calculated by subtracting h(x) from g(x).

So, we have:

$g(x) - h(x) = -\frac74x^\frac12+12x^{-\frac14}-21x^3 - (8x^3+12x^{-\frac12}+6x^\frac14-14x^{-4})$

Open the brackets

$g(x) - h(x) = -\frac74x^\frac12+12x^{-\frac14}-21x^3 - 8x^3-12x^{-\frac12}-6x^\frac14 + 14x^{-4}$

Collect like terms

$g(x) - h(x) = -21x^3 - 8x^3-\frac74x^\frac12-6x^\frac14 +12x^{-\frac14}-12x^{-\frac12}+ 14x^{-4}$

Evaluate the like terms

$g(x) - h(x) = -29x^3-\frac74x^\frac12-6x^\frac14 +12x^{-\frac14}-12x^{-\frac12}+ 14x^{-4}$

Hence, the value of g(x)- h(x) is $-29x^3-\frac74x^\frac12-6x^\frac14 +12x^{-\frac14}-12x^{-\frac12}+ 14x^{-4}$

Read more about composite functions at:

https://brainly.com/question/10687170