You have the following function given in the exercise:
[tex]f\mleft(x\mright)=4\cdot5^x+15x-7[/tex]And the other function is:
[tex]g\mleft(x\mright)=\mleft(-3\mright)\cdot5^x-13[/tex]You need to remember that this means that you must subtract the function g(x) from the function f(x):
[tex]\mleft(f-g\mright)\mleft(x\mright)[/tex]It can also be expressed as following:
[tex]f(x)-g(x)[/tex]Then, you can set up that:
[tex](f-g)(x)=(4\cdot5^x+15x-7)-((-3)\cdot5^x-13)[/tex]In order to simplify, it is important to remember the Sign rules for Multiplication:
[tex]\begin{gathered} -\cdot-=+ \\ +\cdot+=+ \\ -\cdot+=- \\ +\cdot-=- \end{gathered}[/tex]Then, you can distributive the negative sign:
[tex](f-g)(x)=4\cdot5^x+15x-7+3\cdot5^x+13[/tex]Finally, you need to add the like terms (which are defined as those terms that have the same variables and the same exponents):
[tex](f-g)(x)=7\cdot5^x+15x+6^{}[/tex]The answer is:
[tex](f-g)(x)=7\cdot5^x+15x+6^{}[/tex]