Question Type 1: Finding composite functions given two simple functions Exercises

Given $f(x)=2x+5$ and $g(x)=3x^2$, find $(f\circ g)(x)$.

Let $f(x)=\sqrt{2x+1}$ and $g(x)=x^2-3$. Find $(f\circ g)(x)$ and state its domain.

Let $f(x)=6x^2+3$ and $g(x)=x e^x$. Find $(f\circ g)(x)$ and $(g\circ f)(x)$.

Let $f(x)=e^{2x}$ and $g(x)=x^2$. Find $(f \circ g)(x)$ and $(g \circ f)(x)$.

Let $f(x)=\frac{3}{x}$ and $g(x)=1-x$. Find $(f\circ g)(x)$ and $(g\circ f)(x)$.

Let $f(x)=\sqrt{x}$ and $g(x)=x-4$. Find $(f\circ g)(x)$ and $(g\circ f)(x)$.

Let $f(x)=\ln x$ and $g(x)=x^3$. Find $(g\circ f)(x)$.

Let $f(x)=\ln(x-1)$ and $g(x)=e^x+1$. Find $(f\circ g)(x)$.

Let $f(x)=\frac{1}{x}$ and $g(x)=x+2$. Find $(f\circ g)(x)$.

Let $f(x)=\frac{x+2}{x-1}$ and $g(x)=3x$. Find $(f\circ g)(x)$ and $(g\circ f)(x)$.

Given $f(x)=\sin x$ and $g(x)=x^2$, find $(f\circ g)(x)$ and $(g\circ f)(x)$.

Let $f(x)=\sqrt[3]{x}$ and $g(x)=x^2+1$. Find $(f\circ g)(x)$.