Question

If f(x)= x^2-1 and g(x)=2x-3, what is the domain of (fog)(x)

Answer 1

`\large\boxed{\text{The domain is the set of all real numbes}\to x\in\mathbb{R}}`

Explanation:

`f(x)=x^2-1,\ g(x)=2x-3\\\\(f\circ g)(x)-\text{instead of x in the function equation f(x) put}\ 2x-3:\\\\(f\circ g)(x)=(2x-3)^2-1\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(f\circ g)(x)=(2x)^2-2(2x)(3)+3^2-1=4x^2-12x+9-1\\\\(f\circ g)(x)=4x^2-12x+8\\\\\text{the domain is the set of all real numbes}\to x\in\mathbb{R}`