For the functions f(x) = √x + 5, g(x) = 5x − 3, and h(x) = x^2 −3x + 5, find the following and simplify.

Question

For the functions f(x) = √x + 5, g(x) = 5x − 3, and h(x) = x^2 −3x + 5, find the following and simplify:

a. f · g(4)

b. (g of h)(3)

c. (g-h)(x)

d. (f of g)(x)

Answer 1

Part A Multiply f(x) and g(x) = [√(x + 5)](5x - 3) = 5x[√(x + 5)] - 3[√(x + 5)]

Then substitute x with 4. So 20(7) - 3(7) = 119

Part B. To find (g of h) let x in g(x) = h(x) which is x² - 3x + 5

So g(h(x)) = 5(x² - 3x + 5) - 3 = 5x² - 15x + 25 - 3 = 5x² - 15x + 22

Part C. Subtract g(x) - h(x) = (5x - 3) - (x² - 3x + 5) = -x² + 8x - 8

Part D. Let x in f(x) equal g(x) which is 5x - 3. So f(g(x)) = √[(5x - 3) + 5] = √(5x + 2)