Question

f(x)= 2x + 1 g(x)= 3x + 4 f(g(x))= ?

Answer 1

Pretty much saying plug in the function g(x) where ever there is an x in f(x)

Answer 2

Given f(x) = 3x + 2 and g(x) = 4 – 5x,

find (f + g)(x), (f – g)(x), (f×g)(x), and (f / g)(x).
To find the answers, all I have to do is apply the operations (plus, minus, times, and divide) that they tell me to, in the order that they tell me to.

(f + g)(x) = f(x) + g(x) = [3x + 2] + [4 – 5x] = 3x – 5x + 2 + 4 = –2x + 6

(f – g)(x) = f(x) – g(x) = [3x + 2] – [4 – 5x] = 3x + 5x + 2 – 4 = 8x – 2

(f×g)(x) = [f(x)][g(x)] = (3x + 2)(4 – 5x) = 12x + 8 – 15x2 – 10x

= –15x2 + 2x + 8

(f/g)(x) = [f(x)]/[g(x)] = [3x + 2]/[4 - 5x]

Given f(x) = 2x, g(x) = x + 4, and h(x) = 5 – x3,

find (f + g)(2), (h – g)(2), (f × h)(2), and (h / g)(2).
To find the answers, I can either work symbolically (like in the previous example) and then evaluate, or I can find the values of the functions at x = 2 and then work from there. It's probably simpler in this case to evaluate first, so:

f(2) = 2(2) = 4

g(2) = (2) + 4 = 6

h(2) = 5 – (2)3 = 5 – 8 = –3

Now I can evaluate the listed expressions:

(f + g)(2) = f(2) + g(2) = 4 + 6 = 10

(h – g)(2) = h(2) – g(2) = –3 – 6 = –9

(f × h)(2) = f(2) × h(2) = (4)(–3) = –12

(h / g)(2) = h(2) ÷ g(2) = –3 ÷ 6 = –0.5

If you work symbolically first, and plug in the x-value only at the end, you'll still get the same results. Either way will work. Evaluating first is usually easier, but the choice is up to you.

Answer 3

thank you :)

Answer 4

Np ;)