Answer:
1st answer: f(g(5)) =155
2nd answer: f(g(2)) = 255
4th answer: f(g(x)) = 2x + 14.
Explanation:
For 1st one:
Given:
f(x) = 2x + 5
g(x) = 3x²
To find:
f(g(h))=?
Solution:
First, let's solve for the value of the inner function, g(5).
We have g(x) = 3x².
So, g(5) = 3(5)²= 75.
Now we know that g(5) = 75, so we can solve for f(g(5)).
We have f(x) = 2x + 5.
So, f(g(5)) = 2(g(5)) + 5 = 2(75) + 5 = 155.
Therefore, the value of f(g(5)) is 155.

2nd Question:
Given:
f(x) = 4x² - 1 and g(x) = 3x + 2
First, let's solve the value of the inner function, g(2).
We have g(x) = 3x + 2.
So, g(2) = 3(2) + 2 = 8.
Now we know that g(2) = 8, so we can solve for f(g(2)).
We have f(x) = 4x² - 1.
So, f(g(2)) = 4(g(2))² 1 = 4(8)² - 1 = 255.
Therefore, the value of f(g(2)) is 255.

3rd Question:
Let's evaluate the following given f(x) = 4x + 3 and g (x) = 2x - 1.
f(1) = 4(1) + 3 = 7
f(2)= 4(2)+3=11
g(1)=2(1)-1=2-1=1
g(2) = 2(2) - 1 = 3
f(g(1))=f(1) =7
g(f(2)) = g(11) = 2(11) - 1 = 20

4th Question:
Given f(x) = 2x and g(x) = x + 7
To find f(g(x))
Solution:
Substitute the value of g(x) in place of x of f(x)
f(g(x)) = 2(g(x)) = 2(x + 7) = 2x + 14
Therefore, the value of f(g(x)) is 2x + 14.