Math  /  Algebra

QuestionFind composite functions for f(x)=xf(x)=\sqrt{x} and g(x)=8x+1g(x)=8x+1: (a) fgf \circ g, (b) gfg \circ f, (c) fff \circ f, (d) ggg \circ g.

Studdy Solution
The domain of ggg \circ g is the set of all real numbers, because the function 64x+964x+9 is defined for all x-values.
So, the domain of ggg \circ g is (,)(-\infty, \infty).
In conclusion, we have(a) (fg)(x)=8x+1(f \circ g)(x) = \sqrt{8x+1}, domain [18,)[-\frac{1}{8}, \infty)(b) (gf)(x)=8x+1(g \circ f)(x) =8\sqrt{x}+1, domain [,)[, \infty)(c) (ff)(x)=x(f \circ f)(x) = \sqrt{\sqrt{x}}, domain [,)[, \infty)(d) (gg)(x)=64x+9(g \circ g)(x) =64x+9, domain (,)(-\infty, \infty)

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