Evaluating a function

EVALUATING FUNCTIONS

1. Let 𝑓 (𝑥) = 𝑥 − 5𝑥 2 + 4. Find the following:

a) 𝑓 (2)
𝑓 (2) = (2) − 5(2)2 + 4
𝑓 (2) = (2) − 5(4) + 4
𝑓 (2) = 2 − 20 + 4
𝑓 (2) = −14

b) 𝑓 (3.5)
𝑓 (3.5) = (3.5) − 5(3.5)2 + 4
𝑓 (3.5) = (3.5) − 5(12.25) + 4
𝑓 (3.5) = 3.5 − 61.25 + 4
𝑓 (3.5) = −53.75

c) 𝑓 (𝑎 + 1)
𝑓 (𝑎 + 1) = (𝑎 + 1) − 5(𝑎 + 1)2 + 4
𝑓 (𝑎 + 1) = (𝑎 + 1) − 5(𝑎 2 + 2𝑎 + 1) + 4
𝑓 (𝑎 + 1) = 𝑎 + 1 − 5𝑎2 − 10𝑎 − 5 + 4
𝑓 (𝑎 + 1) = −5𝑎2 − 9𝑎

d) 𝑓(√𝑎)
2
𝑓(√𝑎) = (√𝑎) − 5(√𝑎) + 4
𝑓(√𝑎) = (√𝑎) − 5(𝑎) + 4
𝑓(√𝑎) = −5𝑎 + √𝑎 + 4

e) 𝑓 (𝑎2 )
𝑓 (𝑎2 ) = (𝑎 2 ) − 5(𝑎2 )2 + 4
𝑓 (𝑎2 ) = (𝑎 2 ) − 5(𝑎4 ) + 4
𝑓 (𝑎2 ) = −5𝑎4 + 𝑎2 + 4


2. Let 𝑓 (𝑥) = 𝑋 𝑋 + 1 and 𝑔(𝑥) = √𝑥 − 1. Find the following:
a) 𝑓 (1) + 𝑔(1)
𝑓 (1) + 𝑔(1) = (11 + 1) + (√1 − 1)
𝑓 (1) + 𝑔(1) = (1 + 1) + (1 − 1)
𝑓 (1) + 𝑔(1) = 2

b) (𝑓𝑜𝑔)(𝑥)
(𝑓𝑜𝑔)(𝑥) = (√𝑥 − 1)(√𝑥−1) + 1

c) (𝑔𝑜𝑓)(𝑥)
(𝑔𝑜𝑓)(𝑥) = √(𝑋𝑋 + 1) − 1