Question

Suppose that f is a function whose domain is the interval [-5, 5] and that f(x) = x/x + 5 for every x in the interval [0, 5]. Suppose f is an even function. Evaluate f(-3) Enter the exact answer in fraction form if necessary

Answer 1

f(x)=x/(x+5) is shown in part as the red curve for x ∈ (-5,5].

But if we take the interval [0,5] and reflect it in the y axis (blue curve) we can convert it into an even function, such that [-5,0] is a reflection of [0,5].

The rule for even functions is that f(x)=f(-x).

Therefore f(-3)=f(3)=⅜.