Question

If h(x)=(f o g) (x) and h(x)=3√x+3, find g(x) if f(x)=3√x+2?

The 3 is in top the the square root. Please help me! :(

Answer 1

if h(x) = g(x) then putting in f(x) = x will make g(x) = h(x) = g(f(x))

Answer 2

@zzr0ck3r so then would it be 3sqrt x+3+2.....?

Answer 3

are h(x) and g(x) the same thing?

Answer 4

@zzr0ck3r no

Answer 5

\( h(x) = (f\circ g)(x) = f\left(g(x)\right) \)

Answer 6

Now
\( h(x) = 3\sqrt x + 3 \)
and
\(f(x) = 3\sqrtx + 2 \)

so the question is what g(x) will turn f(x) into h(x)?

Answer 7

@LarsEighner so would the overall answer be?
I've done it more than once and keep getting different answers

Answer 8

workin on it

Answer 9

@LarsEighner ok

Answer 10

okay I think this is it

we want u such that

\( 3\sqrt x + 3 = 3 \sqrt u + 2 \)

Answer 11

which is:

\(\begin{align} 3\sqrt x +3 - 2 &= 3\sqrt u \cr \sqrt x - {1\over 3} &= \sqrt u \cr (\sqrt x + 1)^2 = u \end{align}\)

Answer 12

@LarsEighner I thought the outcome was just a plain number, guess I was wrong. Thank you.

Answer 13

so

\( g(x) = (\sqrt x + {1 \over 3})^2 \)

check

\( f(g(x)) = 3 \sqrt{(\sqrt x + {1\over 3})^2} + 2 \)

\( f(g(x)) = 3 \sqrt x + (3){1\over 3} + 2 \)

( f(g(x)) = 3 \sqrt x + 3 \)

which, lo an behold is the same as

\( h(x) = 3 \sqrt x + 3 \)

Answer 14

@LarsEighner Thank you very much. I kept making simple mistakes, I see what I did wrong now.