MATH SOLVE

4 months ago

Q:
# yo can someone help and give me a small follow up to understand the problem?

Accepted Solution

A:

Step-by-step explanation:To find the inverse function, switch x and y and solve for y.a) y = 2^(x − 1) + 1x = 2^(y − 1) + 1x − 1 = 2^(y − 1)log₂(x − 1) = y − 1y = log₂(x − 1) + 1g(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) − 12x + 1 = ln(y/2)e^(2x + 1) = y/2y = 2e^(2x + 1)g(x) is the inverse of f(x).c) y = 4 ln(x²) / e²x = 4 ln(y²) / e²e² 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) − 10x = 10^(y − 10) − 10x + 10 = 10^(y − 10)log₁₀(x + 10) = y − 10y = log₁₀(x + 10) + 10g(x) is not the inverse of f(x).