Question

Find (f -g)(x) if f(x) = 4.5* + 15x - 7 and g(x)=(-3). 5* - 13.

Answer 1

You have the following function given in the exercise:

`f\mleft(x\mright)=4\cdot5^x+15x-7`

And the other function is:

`g\mleft(x\mright)=\mleft(-3\mright)\cdot5^x-13`

You need to remember that this means that you must subtract the function g(x) from the function f(x):

`\mleft(f-g\mright)\mleft(x\mright)`

It can also be expressed as following:

`f(x)-g(x)`

Then, you can set up that:

`(f-g)(x)=(4\cdot5^x+15x-7)-((-3)\cdot5^x-13)`

In order to simplify, it is important to remember the Sign rules for Multiplication:

`\begin{gathered} -\cdot-=+ \\ +\cdot+=+ \\ -\cdot+=- \\ +\cdot-=- \end{gathered}`

Then, you can distributive the negative sign:

`(f-g)(x)=4\cdot5^x+15x-7+3\cdot5^x+13`

Finally, you need to add the like terms (which are defined as those terms that have the same variables and the same exponents):

`(f-g)(x)=7\cdot5^x+15x+6^{}`

The answer is:

`(f-g)(x)=7\cdot5^x+15x+6^{}`