Prove that if f(x) and g(x) are both even functions, then h(x) = f(x) + g(x) is an even function.

yes, it is.

Step-by-step explanation:

An even function is that where for any x, f(-x)=-f(x).

So, suppose that f(x) and g(x) are even functions and define h(x)= f(x)+g(x). Then:

h(-x) = f(-x)+g(-x)

= -f(x)+(-g(x)) because f and g are even functions.

= -f(x)-g(x)

= -(f(x)+g(x))

= -h(x).

Then, h(x) is an even function.

range is infinite on both x and y axis positive and negative

step-by-step explanation:

80° is the measure of gh

step-by-step explanation:

circle f is congruent to circle j

we have two circle with center f and j.

both circles are congruent. the radius of the circle would be equal.

see the attachment for the circle.

we are given ∠efd ≅ ∠gjh

therefore, arc (ed) = arc (gh)     (∴ circle f is congruent to circle j)

but ∠dfe=80°=arc (ed)

therefore, arc (gh) = 80°

thus, 80° is the measure of gh