NZ Level 8 (NZC) Level 3 (NCEA) [In development]

Integration to give log functions

The derivative of $f\left(x\right)$`f`(`x`) is $\frac{1}{x}$1`x`.

Which of the following could be the function? Select all the correct options.

$f\left(x\right)=k\ln x$`f`(`x`)=`k``l``n``x`

A

$f\left(x\right)=\ln\left(\left|kx\right|\right)$`f`(`x`)=`l``n`(|`k``x`|)

B

$f\left(x\right)=\ln kx$`f`(`x`)=`l``n``k``x` for $k<0$`k`<0, $x>0$`x`>0

C

$f\left(x\right)=\ln x$`f`(`x`)=`l``n``x`

D

$f\left(x\right)=\ln kx$`f`(`x`)=`l``n``k``x` for $k>0$`k`>0, $x<0$`x`<0

E

$f\left(x\right)=k\ln x$`f`(`x`)=`k``l``n``x`

A

$f\left(x\right)=\ln\left(\left|kx\right|\right)$`f`(`x`)=`l``n`(|`k``x`|)

B

$f\left(x\right)=\ln kx$`f`(`x`)=`l``n``k``x` for $k<0$`k`<0, $x>0$`x`>0

C

$f\left(x\right)=\ln x$`f`(`x`)=`l``n``x`

D

$f\left(x\right)=\ln kx$`f`(`x`)=`l``n``k``x` for $k>0$`k`>0, $x<0$`x`<0

E

Easy

Approx 2 minutes

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