help solving these questions

[softball1145]

I would appreciate it if somebody could give me the answers to the following problems so that I can see if I am correct with my answer:

questions:

1. Given f(x) = 2x + 5 and g(x) = x^2 + 2x - 3:

. . .A. (f x g)(-1) = f(g(-1))

. . .B. (f x f)(2) = f(f(2))

. . .C. (f x g)(x) = f(g(x))

2. Are the functions f(x) = 4x - 2 and g(x) = 1/4x - 1/2 inverses?

3. Find the inverse of f(x) = 3/4x + 1/4

4. Solve 25^x + 1 = 5^x - 1 by making each side have the same base.

 

[tkhunny]

1) I really hate that notation. I never know what it means.
2) if f(g(x)) = x, they are inverses.
3) y = (3/4)x + 1/4 Swap and solve. Solve x = (3/4)y + 1/4 for x.
4) 25 = 5^2

 

[stapel]

I would appreciate it if somebody could give me the answers to the following problems so that I can see if I am correct with my answer

Better method: You show your work and reasoning, along with your solutions, and the tutors can check them. (FYI: Most of the tutors don't do students' homework for them. Sorry.)

(f x g)(-1) = f(g(-1))

What are the instructions for (A), (B), and (C)? Are you supposed to be multiplying the functional values (the "f × g" notation) or composing them (the "f o g" or "f(g)" notation)?

Thank you.

Eliz.

 

[softball1145]

equations

it is supposed to be the (f o g) notation.
could somebody help me get started with the problems because i just don't understand how to do them.

 

[pka]

\(\displaystyle \
\begin{array}{l}
f \circ g(x) = f(g(x)) \\
\\
f(x) = 2x + 5\quad \& \quad g(x) = x^2 + 2x - 3 \\
\\
f(g(x)) = 2(g(x)) + 5 = 2(x^2 + 2x - 3) + 5 = 2x^2 + 4x - 1 \\
\end{array}\)