if (f(x)=\frac{x - 3}{x}) and (g(x)=5x - 4), what is the domain of ((fcirc g)(x))?\n({x|x\neq0})\n({x|x\neq\f…

if (f(x)=\frac{x - 3}{x}) and (g(x)=5x - 4), what is the domain of ((fcirc g)(x))?\n({x|x\neq0})\n({x|x\neq\frac{1}{3}})\n({x|x\neq\frac{4}{5}})\n({x|x\neq3})

if (f(x)=\frac{x - 3}{x}) and (g(x)=5x - 4), what is the domain of ((fcirc g)(x))?\n({x|x\neq0})\n({x|x\neq\frac{1}{3}})\n({x|x\neq\frac{4}{5}})\n({x|x\neq3})

Answer

Explanation:

Step1: Find the composition $(f\circ g)(x)$

$(f\circ g)(x)=f(g(x))$. Substitute $g(x) = 5x - 4$ into $f(x)$: $f(g(x))=\frac{(5x - 4)-3}{5x - 4}=\frac{5x-7}{5x - 4}$.

Step2: Determine the domain

The domain of a rational - function is all real numbers except the values of $x$ that make the denominator equal to zero. Set the denominator equal to zero: $5x-4 = 0$. Solving for $x$ gives $5x=4$, so $x=\frac{4}{5}$.

Answer:

$\left{x|x\neq\frac{4}{5}\right}$