need help with fcn composition, inverses, etc.

[softball1145]

1. Given f(x) = the square root of x+3 and g(x) = 2x , find (f o g)(2) = f(g(2))

f(4) = the square root of 4+3 = the square root of 7; that is the answer that I got

2. Given f(x) = 2x + 4 and g(x) = 3x^2 - 6,

A. (f o g)(x) = f(g(x))
B. (g o f)(x) = g(f(x))
C. (f o f)(x) = f(f(x))

3. Determine whether (f(g(x)) and g(f(x)) are equal to x.

f(x) = x^2-4 and g(x) = the square root of x-4

4. Given the one-to-one function f(x) = 3/4x+2, find the inverse.

5. Solve the following by making the bases equal on both sides of the equation: 4^x^2-1 = 16

 

[stapel]

1) Is f(x) equal to sqrt[x] + 3, sqrt[x + 3], or something else? Where are you stuck?

2) Plug the expression for the "inner" function in for "x" in the "outer" function. Simplify. For instance:

. . . . .f(x) = x² + 5x, g(x) = 3x - 2:

. . . . .f(g(x)) = f(3x - 2)
. . . . .= [3x - 2]² + 5[3x - 2]
. . . . .= 9x² - 12x + 4 + 15x - 10

...and so forth.

3) Is g(x) equal to sqrt[x] - 4, sqrt[x - 4], or something else? Where are you stuck?

4) Is f(x) equal to 3/(4x) + 2, (3/4)x + 2, 3/(4x + 2), or something else?

The basic process for finding the inverse generally runs like this:

. . . . .a) Rename "f(x)" as "y".
. . . . .b) Solve for "x=".
. . . . .c) Switch x and y, so you now have "y=".
. . . . .d) Rename this new "y" as "f^-1(x)".

How far have you gotten? Where are you stuck?

5) I'm sorry, but I can't figure this one out. Please reply using grouping symbols or LaTeX formatting or some other clarification of your meaning. Showing what you've tried so far will probably help, too.

Thank you.

Eliz.