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Suppose that the functions and g are defined as follows.f(x) = 5x+4g(x) = 4x + 1Find fg and / g. Then, give their domains using interval notation

Suppose That The Functions And G Are Defined As Followsfx 5x4gx 4x 1Find Fg And G Then Give Their Domains Using Interval Notation class=

Sagot :

Given that:

[tex]\begin{gathered} f(x)\text{ = 5x + 4} \\ g(x)\text{ = }\sqrt[]{4x\text{ + 1}} \end{gathered}[/tex]

Solution

1. (f.g)(x)

[tex]\begin{gathered} (fg)(x)\text{ = (5x + 4)(}\sqrt[]{4x+\text{ 1}}) \\ =\text{ 5x(}\sqrt[]{4x+1})\text{ + 4(}\sqrt[]{4x+\text{ 1}}) \end{gathered}[/tex]

The domain of f.g: The domain represents the values of x for which (f.g)(x) is defined

[tex]\text{ Domain : \lbrack}0,\text{ }\infty\rbrack[/tex]

Answer:

f.g = 5x(sqrt(4x + 1) + 4(sqrt(4x + 1))

Domain : [0,positive infinity]

2. (f - g)(x)

[tex]\begin{gathered} (f-g)(x)\text{ = 5x + 4 - (}\sqrt[]{4x+\text{ 1}}) \\ =\text{ 5x + 4 -}\sqrt[]{4x\text{ + 1}} \end{gathered}[/tex]

The domain of f-g:

[tex]\text{Domain : \lbrack}0,\text{ }\infty\rbrack[/tex]

Answer:

f-g : 5x + 4 - sqrt(4x + 1)

Domain : [0, positive infinity]

N.B sqrt means square root

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