Question

F(x) = x + 5
g(x) = 6x
What is the value of fg(3.5)? *

Answer 1

178.5

(see further note for alternative interpretation)

Explanation:

First, we should recognize the shorthand notation:

• (f · g)(a)

which really means:

• f(a) · g(a)

So, the expression (f · g)(3.5) is really:

• f(3.5) · g(3.5)

To find f(3.5), we can plug 3.5 in for x:

f(x) = x + 5

f(3.5) = 3.5 + 5

f(3.5) = 8.5

To find g(3.5), we can again plug 3.5 in for x:

g(x) = 6x

g(3.5) = 6(3.5)

g(3.5) = 21

Finally, we can solve for f(3.5) · g(3.5) using these values:

f(3.5) · g(3.5) = 8.5 · 21

f(3.5) · g(3.5) = 178.5

Note

One could also interpret fg(x) as f(g(x)), in which case the answer would be:

f(g(3.5)) = f(6(3.5))

= 6(3.5) + 5

= 21 + 5

= 26