IDNLearn.com: Your trusted source for finding accurate answers. Find in-depth and accurate answers to all your questions from our knowledgeable and dedicated community members.

If a(x) = 3x + 1 and b(x)= VX-4, what is the domain of (bºa)(x)?
0 (-0,00)
0 (0.00)
O [1,00)
O [4,00)


If Ax 3x 1 And Bx VX4 What Is The Domain Of Bºax 0 000 0 000 O 100 O 400 class=

Sagot :

The domain of [tex]b\,\circ \,a\,(x)[/tex] is [tex][1, +\infty)[/tex].

How to apply composition between functions

The composition of two functions consists in replacing the variable of the former function ([tex]b(x)[/tex]) by the latter function ([tex]a(x)[/tex]). If we know that [tex]b(x) = \sqrt{x-4}[/tex] and [tex]a(x) = 3\cdot x +1[/tex], then the composite function:

[tex]b\,\circ\,a \,(x) = \sqrt{(3\cdot x+1)-4}[/tex]

[tex]b\,\circ\,a\,(x) = \sqrt{3\cdot x-3}[/tex]   (1)

Since the composite function is a square root function, then the domain fulfill the following inequation:

[tex]3\cdot x -3 \ge 0[/tex]

[tex]x \ge 1[/tex]

Hence, the domain of [tex]b\,\circ \,a\,(x)[/tex] is [tex][1, +\infty)[/tex]. [tex]\blacksquare[/tex]

To learn more on functions, we kindly invite to check this verified question: https://brainly.com/question/5245372

Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your questions find answers at IDNLearn.com. Thanks for visiting, and come back for more accurate and reliable solutions.