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
