Question

Assume that the linear function f(x) contains the points f(1) = 5 and f(9) = 37. What is the value of f(f(6))?

Answer 1

101

Explanation:

f(1) = 5 = 4*1 +1

f(9) = 37 = 4*9+1

f(6) = 4*6+1 = 25

f(f(6)) = f(25) = 4*25+1 =101

Answer 2

101

Explanation:

Given the values of a linear function f(1) = 5 and f(9) = 37, you want the value of f(f(6)).

Linear function

The given ordered pairs are (1, 5) and (9, 37). Using these, we can find the slope of the function to be ...

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

m = (37 -5)/(9 -1) = 32/8 = 4

The y-intercept is ...

b = y -mx

b = 5 -4(1) = 1

So the function in slope-intercept form is ...

y = mx +b

f(x) = 4x +1

Application

The value of f(6) is ...

f(6) = 4·6 +1 = 25

The value of f(f(6)) is ...

f(f(6)) = f(25) = 4·25 +1 = 101

The value of f(f(6)) is 101.