1-and-gx-x-2-consider-the-composition-gfx-gfx-1x-1-2-determine-the-domain-of-gfx

Question

Let f(x)=1x−1f(x)=\frac{1}{x-1} and g(x)=x−2g\left(x\right)=\sqrt{x-2}. Consider the composition where: (g∘f)(x)=g(f(x))=1x−1−2(g\circ f)(x)=g(f(x))=\sqrt{\frac{1}{x-1}-2}. Determine the domain of (g∘f)(x)(g∘f)(x).

Accepted Answer

(1,32](1,\frac32]

Answer

(−∞,1)∪(1,∞)(-∞,1) ∪ (1, ∞)

Answer

(32,∞)(\frac32,\infty)

Answer

[1,32][1,\frac32]

Let f(x)=1x−1f(x)=\(\frac{1}{x-1}\) and g(x)=x−2g\(\left\)(x\(\right\))=\(\sqrt{x-2}\). Consider the composition where: (g∘f)(x)=g(f(x))=1x−1−2(g\(\circ\) f)(x)=g(f(x))=\(\sqrt{\frac{1}{x-1}\)-2}. Determine the domain of (g∘f)(x)(g∘f)(x).

Let $f (x) = \frac{1}{x - 1}$ and $g (x) = \sqrt{x - 2}$ . Consider the composition where: $(g \circ f) (x) = g (f (x)) = \sqrt{\frac{1}{x - 1} - 2}$ . Determine the domain of $(g \circ f) (x)$ .