Question

Given f(x) = x + 2, g(x) = 2x + 3, h (x) = 3x + 4 for x E R find (i) fo(goh) (ii) (fog)oh.
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Answer 1

Answer :

(i) fo(goh)(x) = 6x + 13

(ii) (fog)oh(x) = 6x + 13

Solution :

→ Given :

• f(x) = x + 2 , x € R

• g(x) = 2x + 3 , x € R

• h(x) = 3x + 4 , x € R

→ To find :

• fo(goh)(x) = ?

• (fog)oh(x) = ?

(i) fo(goh)(x) = ?

Firstly ,

Let's find goh(x) .

Thus ,

→ goh(x) = g{h(x)}

→ goh(x) = g(3x + 4)

→ goh(x) = 2(3x + 4) + 3

→ goh(x) = 6x + 8 + 3

→ goh(x) = 6x + 11

Now ,

→ fo(goh)(x) = f{goh(x)}

→ fo(goh)(x) = f(6x + 11)

→ fo(goh)(x) = 6x + 11 + 2

→ fo(goh)(x) = 6x + 13

(ii) (fog)oh(x) = ?

Firstly ,

Let's find fog(x) .

Thus ,

→ fog(x) = f{g(x)}

→ fog(x) = f(2x + 3)

→ fog(x) = 2x + 3 + 2

→ fog(x) = 2x + 5

Now ,

→ (fog)oh(x) = (fog){h(x)}

→ (fog)oh(x) = (fog)(3x + 4)

→ (fog)oh(x) = 2(3x + 4) + 5

→ (fog)oh(x) = 6x + 8 + 5

→ (fog)oh(x) = 6x + 13

Hence ,

fo(goh)(x) = (fog)oh(x) = 6x + 13

Answer 2

Answer:

Step-by-step explanation: