(g·f)(5) if f(x)=-13-x2 and g(x)=-14
When calculating compositions of functions, specifically those written in this form, we always work from right to left. We evaluate the right-most function at the independent variable value, so here we start with evaluating f(5):
f(5) = -13-(5)2 = -13 - 25 = -28. Therefore, we have f(5) = -28
Now we take THIS value and place it into the next function in order going from right to left, so this would be evaluating g(-28). Here, we'd do the same substitution idea into the function g, BUT in this case, the function g is just a horizontal line y = -14. No matter which value of x we place into the function "g", the y-value/output will be -14. Therefore, the composition value will be -14.
(g·f)(5) = -14
