SOLUTION: Given the functions {{{f(x) = 6x^2 - 8x - 23}}} and {{{g(x) = 27 - 9x}}}. Find each of the following: g(-4) f(-4) f(5 + h) - f(5)

Algebra ->  Functions -> SOLUTION: Given the functions {{{f(x) = 6x^2 - 8x - 23}}} and {{{g(x) = 27 - 9x}}}. Find each of the following: g(-4) f(-4) f(5 + h) - f(5)      Log On


   

Question 51335: Given the functions f%28x%29+=+6x%5E2+-+8x+-+23 and g%28x%29+=+27+-+9x. Find each of the following:

g(-4)
f(-4)
f(5 + h) - f(5)
Answer by rchill(405) About Me  (Show Source):
You can put this solution on YOUR website!
The notation g(-4) means we take "-4" and substitute it in the g() function anywhere there is "x". So, g%28-4%29+=+27-9%2A%28-4%29+=+27-%28-36%29+=+27%2B36+=+63. Similarly, for function f(), we get . We do the same for f%285+%2B+h%29+-+f%285%29, but have to call the f() function twice: once for (5+h) and the other for (5). Solving f(5+h) produces 6%285%2Bh%29%5E2+-+8%285%2Bh%29+-+23 which simplifies to 6%2A%28h%5E2%2B10h%2B25%29+-40-8h-23, which further simplifies to 6h%5E2%2B60h%2B150-40-8h-23. Combining like terms produces 6h%5E2%2B52h%2B87. Because we solved f(5) earlier to get f%285%29=87, we can now solve f%285+%2B+h%29+-+f%285%29 by substitution: 6h%5E2%2B52h%2B87-87 which simplifies to 6h%5E2%2B52h, which can be rewritten as 2h%2A%283h%2B26%29.