The first step is to find the fuctions, f(x) and g(x)
Since function f(x) is represented by the curve, it's a quadratic function. The curve cuts the x axis at x = 2 and x = - 2. Thus, the factors are (x + 2) and (x - 2). The quadratic function would be
(x + 2)(x - 2)
= x^2 - 2x + 2x - 4
f(x) = x^2 - 4
Since the function g(x) is represented by a straight line, it is a linear function. We would represent the function in the slope intercept form which is expressed as
y = mx + c
where
m = slope
c = y intercept
To find slope, the formula is
m = (y2 - y1)/(x2 - x1)
From the given points,
when x1 = - 2, y1 = 0
when x2 = 2, y2 = 4
m = (4 - 0)/(2 - - 2) = 4/(2 + 2) = 4/4
m = 1
the y intercept is the value of y when x = 0. Thus, c = 2
The function is
g(x) = x + 2
To find (g o f)(x), we would substitute function f into function g. Thus,
gof(x) = x^2 - 4 + 2
gof(x) = x^2 - 2
To find gof(2), we would substitute x = 2 into gof(x). It becomes
gof(2) = 2^2 - 2 = 4 - 2
gof(2) = 2