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For the real values functions f(x) = x + 5 and g(x) = Vx-4, find the composition f g and specify its domain using interval notation.be(2) -

For The Real Values Functions Fx X 5 And Gx Vx4 Find The Composition F G And Specify Its Domain Using Interval Notationbe2 class=

Sagot :

The given functions are

[tex]\begin{gathered} f(x)=x^2+5 \\ g(x)=\sqrt[]{x-4} \end{gathered}[/tex]

We need to find the composite function f(g(x))

Which means, replace x in f(x) by g(x)

[tex]f(g(x))=(\sqrt[]{x-4})^2+5[/tex]

Power 2 will cancel the square root

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

Let us find the domain of f(g(x))

Since there is no square root for a negative number, then

[tex]x-4\ge0[/tex]

Add 4 to both sides, then

[tex]\begin{gathered} x-4+4\ge0+4 \\ x\ge4 \end{gathered}[/tex]

Then the domain of f(g(x)) should be

[tex]\lbrack4,\infty)[/tex]

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