Question

Explain how to evaluate f(g(0)).

Answer 1

Answer as a fraction:  17/6

Answer in decimal form: 2.8333  (approximate)

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Work Shown:

Let's use the two black points to determine the equation of the red f(x) line.

Use the slope formula to get...

m = slope

m = (y2-y1)/(x2-x1)

m = (4-0.5)/(2-(-1))

m = (4-0.5)/(2+1)

m = 3.5/3

m = 35/30

m = (5*7)/(5*6)

m = 7/6

Now use the point slope form

y - y1 = m(x - x1)

y - 0.5 = (7/6)(x - (-1))

y - 0.5 = (7/6)(x + 1)

y - 0.5 = (7/6)x + 7/6

y = (7/6)x + 7/6 + 0.5

y = (7/6)x + 7/6 + 1/2

y = (7/6)x + 7/6 + 3/6

y = (7/6)x + 10/6

y = (7/6)x + 5/3

So,

f(x) = (7/6)x + 5/3

We'll use this later.

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We ultimately want to compute f(g(0))

Let's find g(0) first.

g(0) = 1 since the point (0,1) is on the g(x) graph

We then go from f(g(0)) to f(1). We replace g(0) with 1 since they are the same value.

We now use the f(x) function we computed earlier

f(x) = (7/6)x + 5/3

f(1) = (7/6)(1) + 5/3

f(1) = 7/6 + 5/3

f(1) = 7/6 + 10/6

f(1) = 17/6

f(1) = 2.8333 (approximate)

This ultimately means,

f(g(0)) = 17/6 as a fraction

f(g(0)) = 2.8333 as a decimal approximation