Question

!URGENT HELP! 100 points to any who are willing ^-^

Consider the function f(x) =
`2^(x)`. Find b so that the graphs of each of the functions listed are the same as the graph of function f.
•
`g(x) = 4^(bx)`
•
`h(x) = 8^(bx)`
•
`j(x) = ((1)/(2)) ^(bx)`

Side note:
To whom it may concern!
I do deeply appreciate all your help if you did or were willing to help me! Thank you for taking the time out of your day and life to bring aid to my little situation! Bless your kind soul.

Answer 1

To find b, we need to make sure that g(x), h(x), and j(x) have the same graph as f(x).

For g(x), we have:
g(x) = 4^bx = (2^2)^bx = 2^(2bx)
Since 2^x = f(x), we can set 2bx = x to find b. Solving for b, we get:
b = 1/2

For h(x), we have:
h(x) = 8^bx = (2^3)^bx = 2^(3bx)
Since 2^x = f(x), we can set 3bx = x to find b. Solving for b, we get:
b = 1/3

For j(x), we have:
j(x) = (1/2)^bx = 2^(-bx)
Since 2^x = f(x), we can set -bx = x to find b. Solving for b, we get:
b = -1

So, for g(x) = 4^bx, b = 1/2; for h(x) = 8^bx, b = 1/3; and for j(x) = (1/2)^bx, b = -1.