Calculus/Pre-Cal

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Expert: - 8/9/2009


Question
Can you please answer these and show a few steps to help me understand. I have school tomorrow, and I was told that this kind of thing is what we'll be doing.

Identify the parent function and identify any transformations.

3) f(x) = x2 + 1

4) g(x) = x − 3 + 2

5) h(x) = -|X+2| +1

6) find g -1 (x)


Answer
3) f(x) = x2 + 1

4) g(x) = x − 3 + 2

5) h(x) = -|X+2| +1

6) find g -1 (x)

From what I read about them, it seems to me I can say the following:

For 3, I would say the parent function is x^3.
After you cube x, the transformation is adding 1.

For 3, I would simplify first.
g(x) = x - 3 + 2 is the same as g(x) = x - 1.
There parent function is x.
The transformation is to subtract 1.

For 5, the parent funciton is x+2.
After that, the first transformation is to take the absolute value.
The second transformation is to multiply that by -1.
The third transformation is to add 1.

For 6, we just determined g(x) = x -1.
To find the inverse, replace the g(x) with a y and solve for x.
That gives us y = x - 1, so y + 1 = x.
Let us say that the inverse of g(x) is m(y), and m(y) = y + 1.

Maybe m(y) looks like my function (without the parenthesis, anyway).

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