Question

If F(x) = 8x + 7 and g(x) = Vx + 2,
what is (f ° g) (2)?

Answer 1

`fog(2) = 16V+23`.

Explanation:

This is a problem of combination of functions. Let's find the combination of f(x) and g(x).

1. Write the full argument of f(x).

`f(x) = 8x + 7`

2. Insert the argument of g(x) as if it was an x value on f(x).

Argument of g(x): Vx + 2.

`fog(x) = 8(Vx + 2) + 7`

3. Apply the associative property of multiplication to solve the parenthesis.

`fog(x) = [(8)(Vx)+(8)(2)]+ 7\\ \\fog(x) = 8Vx+16+ 7\\ \\fog(x) = 8Vx+23`

4. Insert the given value (2) as x in fog(x).

`fog(2) = 8V(2)+23`

5. Simplify.

`fog(2) = 16V+23`.