C3 Functions Help

I was doing the Edexcel C3 Jan 2010 exam paper and on question 9iib) it asks:

The functions f and g are defined by f(x)= e^(2x) +3 xER
g(x)= ln(x-1) xER x>1

Find fg and state its range:

I found that fg was e^(ln(x-1)^2) +3 but I couldnt find the range, and on exam solutions it says that that is equal to (x-1)^2 +3 but i dont understand how theyve got rid of the natural log and the e?? :s-smilie:

I know how to find the range from (x-1)^2 +3 but i dont know how it was simplified to that. (sorry if its badly worded)

Thanks :colondollar:

Reply 1

TeeEm

19

Original post by abimoon

I was doing the Edexcel C3 Jan 2010 exam paper and on question 9iib) it asks:

The functions f and g are defined by f(x)= e^(2x) +3 xER
g(x)= ln(x-1) xER x>1

Find fg and state its range:

I found that fg was e^(ln(x-1)^2) +3 but I couldnt find the range, and on exam solutions it says that that is equal to (x-1)^2 +3 but i dont understand how theyve got rid of the natural log and the e?? :s-smilie:

I know how to find the range from (x-1)^2 +3 but i dont know how it was simplified to that. (sorry if its badly worded)

Thanks :colondollar:

e^2ln(x-1) = e^ln(x-1)² = (x-1)²

Reply 2

abimoon

OP

Original post by TeeEm

e^2ln(x-1) = e^ln(x-1)² = (x-1)²

thanks but i still dont understand the second step where the natural log and the e were cancelled, how do they cancel out?

Reply 3

Dexterous

14

Original post by abimoon

I was doing the Edexcel C3 Jan 2010 exam paper and on question 9iib) it asks:

The functions f and g are defined by f(x)= e^(2x) +3 xER
g(x)= ln(x-1) xER x>1

Find fg and state its range:

I found that fg was e^(ln(x-1)^2) +3 but I couldnt find the range, and on exam solutions it says that that is equal to (x-1)^2 +3 but i dont understand how theyve got rid of the natural log and the e?? :s-smilie:

I know how to find the range from (x-1)^2 +3 but i dont know how it was simplified to that. (sorry if its badly worded)

Thanks :colondollar:

The Ln and e cancel, when you take e^ln(x) it just becomes x. Just like if you took ln(e^x) it would again become x as they cancel. Remember ln is to the base e so, what power of "e" gives "e"? 1 therefore they cancel.