If f(x) = 2(x - 3)\(^2\) + 3(x - 3) + 4 and g(y) = \(\sqrt{5 + y}\), find g [f(3)] and f[g(4)].

Ann_e

1 year ago

We are given two functions:
• f(x) = 2(x - 3)^2 + 3(x - 3) + 4
• g(y) = \sqrt{5 + y}

We are to find:
1. g[f(3)]
2. f[g(4)]

Step 1: Compute f(3)

Plug x = 3 into f(x) :

f(3) = 2(3 - 3)^2 + 3(3 - 3) + 4 = 2(0)^2 + 3(0) + 4 = 0 + 0 + 4 = 4

Now:

g[f(3)] = g(4)

Step 2: Compute g(4)

g(4) = \sqrt{5 + 4} = \sqrt{9} = 3

So,

g[f(3)] = 3

Step 3: Compute f[g(4)]

First, find g(4) again (same as above):

g(4) = \sqrt{9} = 3

Now find f(3) (already done above):

f(3) = 4

Final Answers:
• g[f(3)] = 3
• f[g(4)] = 4

Correct Option A: 3 and 4

Ayane.9

2 years ago

The explanation is incorrect. When (x-3)^2 is expanded it gives x^2 - 6x + 9. so, when the function is fully simplified it should be 2x^2 - 9x + 13

SammyKush011

6 years ago

Question not well structured
"2(x-3)2"??