Given: F(x) = 5x - 6 and G(x) = x - 4
(FoG) -1 =
F(x) = 3x^2 + 1, G(x) = 2x - 3, H(x) = x
F(3) = 3(3)^2 + 1 = 27 + 1 = 28
G(4) = 2(4) - 3 = 8 - 3 = 5
2H(5) = 2(5) = 10
F(3) + G(4) - 2H(5) = 28 + 5 - 10
F(3) + G(4) - 2H(5) = 23
question 2
Given: F(x) = 5x - 6 and G(x) = x - 4
(FoG) (x) = F(G(x)) = 5(x-4) - 6
= 5x - 20 - 6
= 5x - 26
Inverse
x = 5y - 26
5y = x + 26
y = x/5 + 26/5
So
(FoG) -1 (x) = x/5 + 26/5
A composite function is the combination of more than one functions to form another function.
The results of the computations is as follows:
(1) Given that:
[tex]F(x) = 3x^2 + 1[/tex]
[tex]G(x) = 2x - 3[/tex]
[tex]H(x) = x[/tex]
To calculate F(3) + G(4) - 2H(5)
First, calculate F(3)
[tex]F(x) = 3x^2 + 1[/tex]
[tex]F(3) = 3 \times 3^2 + 1 = 28[/tex]
Next, calculate G(4)
[tex]G(x) = 2x - 3[/tex]
[tex]G(4) = 2 \times 4 - 3 = 5[/tex]
Next, calculate H(5)
[tex]H(x) = x[/tex]
[tex]H(5) = 5[/tex]
So, we have:
[tex]F(3) + G(4) - 2H(5) = 28 + 5 - 2 \times 5[/tex]
[tex]F(3) + G(4) - 2H(5) = 23[/tex]
(2) Given
[tex]F(x) = 5x - 6[/tex]
[tex]G(x) = x - 4[/tex]
First, we calculate (F o G)(x)
[tex](F\ o\ G)(x) = F(G(x))[/tex]
Given that:
[tex]F(x) = 5x - 6[/tex]
Replace x with G(x)
[tex]F(G(x)) = 5 \times G(x) - 6[/tex]
Substitute [tex]G(x) = x - 4[/tex]
[tex]F(G(x)) = 5 \times [x - 4] - 6[/tex]
So, we have:
[tex](F\ o\ G)(x) = 5 \times [x - 4] - 6[/tex]
Substitute -1 for x
[tex](F\ o\ G)(-1) = 5 \times [-1 - 4] - 6[/tex]
[tex](F\ o\ G)(-1) = 5 \times [-5] - 6[/tex]
[tex](F\ o\ G)(-1) = -31[/tex]
Read more about composite functions at:
https://brainly.com/question/10830110
