Resolved: "Find functions fand g such that h=g∘f (Note:..."

High School
Calculus and Analysis
Calculus 1
Analyzing functions

Cabiolab

Answered question

2021-10-10

Find functions fand g such that
$h = g \circ f$
(Note: The answer is not unique. Enter your answers as a comma-separated list of functions. Use non- identity functions for fand g.)
$h (x) = {(5 x^{2} - 8)}^{- 3}$

Answer & Explanation

Benedict

Skilled2021-10-11Added 108 answers

Step 1
Given,
$h = g \cdot f$
$h (x) = {(5 x^{2} - 8)}^{- 3}$
Step 2
Now,
$h = g \cdot f K$
$\Rightarrow h = g (f (x))$
$∴ h (x) = {(5 x^{2} - 8)}^{- 3}$
$\Rightarrow h (x) = \frac{1}{{(5 x^{2} - 8)}^{3}}$
Since, the cube is on , then the is put inside the cube. So, we need to take x, do to it and then take the cube of the result.
$g (x) = \frac{1}{x^{3}}$ , $f (x) = 5 x^{2} - 8$
$∴ h (x) = \frac{1}{{(5 x^{2} - 8)}^{3}} = {(5 x^{2} - 8)}^{- 3}$
Answer $∴ f (x) = 5 x^{2} - 8, g (x) = \frac{1}{x^{3}}$

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