Question

BRAINIEST ANSWER QUICKKKK!!!!! Which of these pairs of functions are inverse functions use: a b c or d

Answer 1

We'll call the result of the original function f and the argument g for sanity.

f = 2^{g-1} + 1

f-1 = 2^{g-1}

log2 (f-1) = g-1

g = 1 + log2 (f-1)

Not a, wrong sign on the -1 at the end.

f = 1/2 (ln(g/2) -1 )

2f = ln(g/2) -1

2f + 1 = ln(g/2)

g/2 = e^{2f + 1}

g = 2 e^{2f + 1}

b is a good pair of inverses, at least over the domain of the logarithm.

f = 4 ln(g^2)/e^2

fe^2 = 4 ln(g^2)

fe^2/4 = ln g^2

g^2 = e^{(fe^2)/4}

Now we take the square root so 

$g = \pm \sqrt{ e^{(fe^2)/4} }$

The $\pm$  is telling us f is not one-to-one on its domain so doesn't have a true inverse.

f = 10^{g-10} - 10

f + 10 = 10^{g-10}

log(f+10) = g-10

g = 10 + log(f+10)

wrong sign again.

I'll go with choice B.