Answer:
- f(g(f(1))) = 45 — needs to use the equation
- g(f(g(0))) = 3
Explanation:
You want to use the graph to evaluate the compositions ...
where f(x) = x² -2x -3, and g(x) = x -2.
Reading the graph
To find the value of a graphed function, locate the function argument on the x-axis and find the point of intersection of that vertical line with the graph. The y-coordinate of that point is the function value.
f(g(f(1)))
Here, we're asked to read the graph to find f(1), use that value to find g(f(1)), then use that value to find f(g(f(1))). This last value is f(-6), which is off the top of the graph. We need to use the equation to find the value:
f(x) = (x -2)x -3
f(-6) = (-6 -2)(-6) -3 = 48 -3 = 45
The value of f(g(f(1))) is 45. The equation must be used for this.
g(f(g(0)))
Reading the graph for g(0), we find the value to be -2. Then f(-2) is 5, and g(5) is 3.
The value of g(f(g(0))) is 3.
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Additional comment
A suitable calculator or spreadsheet can evaluate these expressions for you.