Question

Can someone please help me

Answer 1

Explanation:

For y=g(x) and y = f(x), we can set f(x) = g(x) and go from there.

`4(2)^(-x) +3 = 8-2^(x)\\4 (2)^(-x) - 5 = -2^(x)\\`

Here, we simply subtracted 8 from both sides

Next, we can substitute u in for 2^x to get

4 * (1/u) - 5 = -u

4/u - 5 = -u

Multiply both sides by u

4 - 5u = -u²

Add u² to both sides

u² -5u +4 = 0

Factor

(u-4)(u-1) = 0

We now know that our solutions to this are u = 4 and u = 1, so we must figure out when 2^x = 4 and 2^x = 1. We can then figure out that 2² = 4 and 2^0 = 1, so our answers are 2 and 0 for the second question.

For the first, we can simply plug 2 and 0 into f(x) to get (2,4) and (2,7) as our answers