# If f(x) = 4 – x^{2} and g(x) = 6x, which Expression is Equivalent to (g – f)(3)?

We will use the concept of functions to solve this.

## Answer: If f(x) = 4 – x^{2} and g(x) = 6x, then (g – f)(3) = 23.

Let us solve it step by step.

**Explanation:**

Given that, f(x) = 4 – x^{2} and g(x) = 6x,

Both f(x) and g(x) are function of x and depend on x.

(g – f)(x) = g(x) - f(x)

Substituting the values of g(x) and f(x) we get,

= 6x - (4 - x^{2})

= 6x - 4 + x^{2}

= x^{2} + 6x - 4

Solve this for x = 3 now:

(g – f)(x) = x^{2} + 6x - 4

⇒ (g – f)(3) = (3)^{2} + 6(3) - 4

⇒ (g – f)(3) = 9 + 18 - 4

⇒ (g – f)(3) = 23