The equivalent expression is (g - f) (3) = 23
Solution:
Given that,
[tex]f(x) = 4 - x^2\\\\g(x) = 6x[/tex]
To find: (g - f)(3)
We know that,
(g - f)(x) = g(x) - f(x)
Substituting values we have:
[tex](g - f) (x) = (6x) - (4 - x ^ 2)[/tex]
Rewriting we get,
[tex](g - f) (x) = x ^ 2 + 6x - 4[/tex]
Now let us evaluate for x = 3
Substitute x = 3 in above equation
[tex](g - f) (3) = 3^ 2 + 6(3) - 4\\\\(g - f) (3) = 9 + 18 - 4\\\\(g - f) (3) = 23[/tex]
Therefore the equivalent expression is (g - f) (3) = 23
