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Composition and Inverse Essay

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Below is an essay on "Composition and Inverse" from Anti Essays, your source for research papers, essays, and term paper examples.

Composition and Inverse
Janice Reyes
May 26, 2014

Composition and Inverse
The following functions will be used in this week’s assignment.
2. gx=x2-3
3. hx=7-x3

f-h(4)- Original expression
f4-h4- Rewritten
24+5-7-43 - Substitute 4 for x
8+5- 33 - Simplify
13-1- Simplify further
The second problem involves composing two pairs into each other.
f°g(x)- Original expression
f(gx)- Rewritten so that rule of f will apply
fx2-3- g inserted
2x2-3+5- f applied to g
2x2-6+5- Simplified
2x2-1- Solution
The third problem also involves composing two pairs into each other.
h°g(x)- Original expression
h(g(x))- Rewritten so that rule of h will apply to g
hx2-3- g inserted
7-(x2-3)3- h applied to g
21-3(x2-3)- Multiply numerator and denominator by 3
21-3x2-9- Simplified
12-3x2- Simplified
-3x2+12- Rewritten
x2+4- Solution
The fourth problem involves transforming the function gx=(x2-3) so that it appears on a different x and y axis. In order to transform the g(x) function six points to the right and seven down, we must modify the equation in the following way: gx=(x2-3) - Original function
gx=((x-6)2-3) - Subtracting six from x will transform the function six spaces to the right gx=x-62-3-7 - Subtracting seven from the entire function will transform the function seven spaces down Lastly, we must find the inverse of both f and h. To do so, we will simply rewrite the function with y instead of the function name, switch y and x and then solve for y. Then we will rename y again to the inverse function name to solve. To solve: f-1(x)

fx=2x+5- Original function
y=2x+5 - Rewritten with y replacing function name
x=2y+5 - Rewritten with x and y transposed
2y=x-5 - Solving for y
y=x-52- Solved for y
f-1x=x-52 - Solved.
To solve h-1(x):
hx=7-x3 - Original function
y=7-x3 - Rewritten with y replacing function name
x=7-y3 - Rewritten with x and y transposed
3x=7-y - Multiply both sides by 3
-y=3x-7 - Isolate y...

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