Question

If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (g - f)(3)?

Answer 1

The equivalent expression is (g - f) (3) = 23

Solution:

Given that,

$f(x) = 4 - x^2\\\\g(x) = 6x$

To find: (g - f)(3)

We know that,

(g - f)(x) = g(x) - f(x)

Substituting values we have:

$(g - f) (x) = (6x) - (4 - x ^ 2)$

Rewriting we get,

$(g - f) (x) = x ^ 2 + 6x - 4$

Now let us evaluate for x = 3

Substitute x = 3 in above equation

$(g - f) (3) = 3^ 2 + 6(3) - 4\\\\(g - f) (3) = 9 + 18 - 4\\\\(g - f) (3) = 23$

Therefore the equivalent expression is (g - f) (3) = 23