Variable Expressions as Inputs of Function: Question 1

Question

The functions f and g are defined as follows.

f (x) = x² + 9x + 5 and g (x) = 3 / x² - 2

Find f (x-3) and g (- 5 / x).

Write your answers without parentheses and simplify them as much as possible.

f (x - 3) =

g (- 5 / x) =

Answer 1

f(x) = x^2 +9x +5

f(x-3) = (x-3)^2 +9(x-3) +5 = x^2 -6x +9 +9x -27 +5

= x^2 +3x -13

g(x) = 3/x^2 -2

g(-5/x) = 3/(-5/x)^2 -2 = [3/(25/x^2)] -2 = 3x^2/25 - 50/25

= (3x^2 -50)/25

but maybe you really meant

g(x) =3/(x^2-2), then

g(-5/x) = 3/((-5/x)^2 -2) = 3/(25/x^2 -2) = 3/(25-2x^2)/x^2

= 3x^2/(25-2x^2)

Answer 2

f (x) = x² + 9x + 5

To find f (x - 3), plug in (x-3) for x

f (x-3) = (x-3)² + 9(x-3) + 5 Now simplify

f (x-3) = (x-3)(x-3) + 9(x-3) + 5 FOIL and distribute

f (x-3) =x²-3x-3x+9+9x-27+5 Combine like terms

f (x-3) =x²+3x-13

The same process works for the other problem as well.