Create two functions h(x) and j(x) so that the composed function (h . j)(x) does not exist. Explain your answer.

Question

Create two functions h(x) and j(x) so that the composed function (h  j)(x) does not exist. Explain your answer.

Grade 12 Advanced Functions

Please answer clearly and neatly. Thanks :)

Answer 1

Hello Math H,

here's another of many examples that can fit the requirements. Suppose h(x) = 1/(x - 1) and j is the constant function j(x) = 1

Then h(j(x)) becomes 1/0, which is undefined.

Enjoy!

Answer 2

Hi,

All we have to do is come up with one function j(x) that has a range of outputs that are outside the domain of some other function h(x).

The natural log function, ln(x) is for example only defined for x > 0. So now we just have to find some other function that has a range of values that are R < 0 in order to make the logarithmic function undefined. An example of this is -e^x. All output values of -e^x are negative.

So if h(x) = ln(x) and j(x) = -e^x , then h(j(x)) = ln(-e^x) is undefined for all x