College Algebra

Question

Let ƒ(x) = 4x-3, g(x) = x^2+4, and h(x) = x+5, and find the following.      1. (g*h)(-2)          2. (f+g)(-4)       3. (g/f)(2)       4. (g-fh)(-5)

Answer 1

Hi Kerry.

 

These are function operations and a generic answer could be found for each of these in terms of x, but with the x's given to you, these are much easier.  

 

The key is knowing that (g*h)(x) =g(x) * h(x).  

    (g*h)(-2) = g(-2) * h(-2) = [(-2)²+4] * [(-2) + 5] = 8 * 3 = 24

 

Also (f + g)(x) = f(x) + g(x)   so

      (f + g)(-4) = [4(-4) - 3]+ [(-4)² + 4] = -19 + 20 = 1

 

Again (g/f)(x) = g(x)/f(x)  so

       (g/f)(2) = [2² + 4] / [4(2) - 3]  = 8 / 5  =  1.6

 

Likewise:  (g-fh)(x) = g(x) - f(x)*h(x)   so

         (g-fh)(-5) = g(-5) - f(-5)*h(-5)    (remember the parenthesis first, then multiplication, then do the subtraction)

                        = [(-5)² + 4] - [4(-5) - 3]*[(-5) + 5]

                        = 29 - (-23)(0) = 29

 

Hope that helped.

Vicki