Given: f(x) = 3x 2 + 1, g(x) = 2x - 3, h(x) = x find: f(3) + g(4) - 2h(5) =question 2 given: f(x) = 5x - 6 and g(x) = x - 4 (fog) -1 =

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:

To calculate F(3) + G(4) - 2H(5)

First, calculate F(3)

Next, calculate G(4)

Next, calculate H(5)

So, we have:

(2) Given

First, we calculate (F o G)(x)

Given that:

Replace x with G(x)

Substitute

So, we have:

Substitute -1 for x

Read more about composite functions at:

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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

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this