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).
