They are asking me to find the inverse of the function. I am a little confused, but this is the answer I got, but I'm not sure if its correct. I got f^-1(x) = (Ln(x) + 5) + 5. Is this correct? If not can someone please help show me how to solve this?
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if f(x) = e^(x - 5) - 5
y = e^x/(e^5) - 5 multiply by e^5
y.e^5 = e^x - 5.e^5 add 5.e^5
e^x = y.e^5 + 5.e^5
e^x = e^5(y + 5) since ln(e^x) = x, logs of both sides
x = ln(e^5(y + 5)) since ln(a.b) = ln(a) + ln(b)
x = ln(e^5) + ln(y + 5) since ln(e^x) = x,
x = 5 + ln(y + 5)
y = e^x/(e^5) - 5 multiply by e^5
y.e^5 = e^x - 5.e^5 add 5.e^5
e^x = y.e^5 + 5.e^5
e^x = e^5(y + 5) since ln(e^x) = x, logs of both sides
x = ln(e^5(y + 5)) since ln(a.b) = ln(a) + ln(b)
x = ln(e^5) + ln(y + 5) since ln(e^x) = x,
x = 5 + ln(y + 5)