Yo can someone and give me a small follow up to understand the problem?

Step-by-step explanation:

To find the inverse function, switch x and y and solve for y.

a) y = 2^(x − 1) + 1

x = 2^(y − 1) + 1

x − 1 = 2^(y − 1)

log₂(x − 1) = y − 1

y = log₂(x − 1) + 1

g(x) is not the inverse of f(x).

b) y = ½ (ln(x/2) − 1)

x = ½ (ln(y/2) − 1)

2x = ln(y/2) − 1

2x + 1 = ln(y/2)

e^(2x + 1) = y/2

y = 2e^(2x + 1)

g(x) is the inverse of f(x).

c) y = 4 ln(x²) / e²

x = 4 ln(y²) / e²

e² x = 4 ln(y²)

e² x / 4 = ln(y²)

y² = e^(e² x / 4)

y = e^(e² x / 8)

g(x) is the inverse of f(x).

d) y = 10^(x − 10) − 10

x = 10^(y − 10) − 10

x + 10 = 10^(y − 10)

log₁₀(x + 10) = y − 10

y = log₁₀(x + 10) + 10

g(x) is not the inverse of f(x).

the answers are in the images, i received 100% on this assignment. hope this !