Composition and Inverse

Only available on StudyMode
  • Topic: Inverse function, Function, Exponentiation
  • Pages : 2 (486 words )
  • Download(s) : 329
  • Published : March 3, 2013
Open Document
Text Preview
Composition and Inverse

This week we have been assigned three functions which we must evaluate. These are the functions which we have to evaluate this week. fx=2x+3 gx=x2-3 hx=7-x3 We have been asked to compute(f-h)(4).

So we can evaluate each separately and then subtract.
=33=1 h4=1
This is our final answer.
Next we are to compare two pairs of the functions into each other. First we will work out. f°gx=f(gx) This means the rule of f will work on g.
=fx2-3 Here f is now going to work on the rule of g. =2x2-3+5 The rule of f is applied to g.
=2x2-6+5 Simplifying
f°gx=2x2-1 The final results.

Now we will compose the following:
h°gx=h(gx) The rule of h will work on g.
=-7+(x2-3)3 The rule of h is applied to g. h°gx=-10+x23 The final results.

Next we are asked to transform g(x) so that the graph is placed 6 units to the right and 7 units downward for where it would be right now. * Six units to the right means to put a -6 in with x to be squared. * Seven units downward means to put -7 outside of the squaring. * The new functions will look like this:

Our last job is to find the inverse of two of our functions, f and h. To find the inverse we will write the function with y instead of the function name, then we will switch the places of x and y, and solve for y again. Here are the functions: fx=2x+3 hx=7-x3

Here we replace f(x) and h(x) with y:
y=2x+3 y=7-x3
Here we switch the y and the x:
x=2y+3 x=7-y3
Now we solve for y:
Subtract 3 from both sides. Multiply both sides by 3. -3+x=2y 3x=7-y
One more solving...
tracking img